New modular non-hyperelliptic genus 3 curves

Label $ C: \,\,\,\,\,\,F(x,y,z)\,\,=\,0 $
$ C^A_{{20,A}_{\{ 1, 1 \}}}$ $ x^3z - x^2y^2 - 3x^2z^2 + xy^3 + 4xz^3 - 2z^4=0$
$ C^A_{{24,A}_{\{ 0, 1, 0 \}}}$ $ x^3 z - x^2 y^2 - x^2 z^2 + x y^3 - x y^2 z - 3 x y z^2 + y^3 z + 2 y^2 z^2 + y z^3=0$
$ C^A_{{24,A}_{\{ 1, 1, 1 \}}}$ $ x^3 z - 2 x^2 y z - x^2 z^2 - x y^3 + 2 x y^2 z + 6 x y z^2 + 2 y^3 z - 2 y^2 z^2 - 4 y z^3=0$
$ C^A_{{36,A}_{\{ 1, 3 \}}}$ $ x^3 z - 3 x^2 z^2 - x y^3 + 4 x z^3 + 2 y^3 z - 2 z^4=0$
$ C^A_{{39,A}_{\{ 0, 6 \}}}$ $ x^3 z - 2 x^2 z^2 + 4 x y^2 z - 7 x y z^2 - 6 x z^3 - y^4 + 5 y^3 z + 2 y^2 z^2 - 6 y z^3 - 3 z^4=0$
$ C^A_{{39,A}_{\{ 0, 4 \}}}$ $ x^3 z - 2 x^2 y z - x y^3 - 2 x y^2 z + 2 x y z^2 + y z^3=0$
$ C^{A,B}_{43}$ $ 2 x^3 z - 2 x^2 y^2 - 6 x^2 z^2 + x y^3 + 9 x y^2 z - 5 x y z^2 + 11 x z^3 - 9 y^4 + 12 y^3 z - 22 y^2 z^2 + 12 y z^3 -9 z^4=0$
$ C^A_{{45,A}_{\{ 2, 0 \}}}$ $ x^3 z + 2 x^2 y z - x y^3 + 2 x y^2 z - 2 x y z^2 + y z^3=0$
$ C^A_{{49,A}_{\{ 14 \}}}$ $ x^3 z - x y^3 + y z^3=0$
$ C^A_{{56,A}_{\{ 0, 1, 0 \}}}$ $ x^3 z + 2 x^2 y z - x^2 z^2 - x y^3 - 2 x y^2 z - 6 x y z^2 + 2 y^3 z + 2 y^2 z^2 + 4 y z^3=0$
$ C^{A,B,C}_{57}$ $ 2 x^3 z - 2 x^2 y^2 + 5 x^2 z^2 - 16 x y^2 z - 8 x y z^2 + 2 x z^3 + 3 y^4 + 8 y^3 z - 6 y^2 z^2 - 4 y z^3=0$
$ C^{A,B}_{65}$ $ 2 x^3 z - 2 x^2 y^2 - 7 x^2 z^2 - 2 x y^3 - 4 x y^2 z + 26 x y z^2 + 30 x z^3 - 3 y^4 - 26 y^3 z - 81 y^2 z^2 - 98 y z^3 - 40 z^4=0$
$ C^{A,C}_{65}$ $ 6 x^3 z - 6 x^2 y^2 - 8 x^2 z^2 - 3 x y^3 + 25 x y^2 z - 13 x y z^2 + 25 x z^3 -11 y^4 + 19 y^3 z - 33 y^2 z^2 + 13 y z^3 - 14 z^4=0$
$ C^{A,B}_{82}$ $ x^3 z - x^2 y^2 - 2 x^2 z^2 + 4 x y^2 z + 3 x y z^2 + y^3 z - 2 y z^3=0$
$ C^{A,C}_{91}$ $ x^3 z - x^2 y^2 - x^2 z^2 + x y^3 - x y^2 z + 3 x y z^2 - x z^3 - 2 y^4 + 4 y^3 z - 6 y^2 z^2 + 4 y z^3 - z^4=0$
$ C^A_{97}$ $ x^3 z - x^2 y^2 - 5 x^2 z^2 + x y^3 + x y^2 z + 3 x y z^2 + 6 x z^3 - 3 y^2 z^2 - y z^3 - 2 z^4=0$
$ C^{A,C,D}_{99}$ $ x^3 z - 3 x^2 z^2 + 3 x y^2 z - 3 x y z^2 + 9 x z^3 - y^4 - 6 y^2 z^2 + y z^3 - 8 z^4=0$
$ C^B_{109}$ $ x^3 z - 2 x^2 y z - x^2 z^2 - x y^3 + 6 x y^2 z - 6 x y z^2 + 3 x z^3 + y^4 -6 y^3 z + 10 y^2 z^2 - 5 y z^3=0$
$ C^C_{113}$ $ x^3 z - x^2 y^2 - 4 x^2 z^2 + x y^3 + 2 x y^2 z + 6 x z^3 - y^3 z - 3 y^2 z^2 + y z^3 - 3 z^4=0$
$ C^{A,C,D}_{118}$ $ x^3 z - x^2 y^2 - x^2 z^2 + 2 x y^2 z + x y z^2 + x z^3 + y^3 z + y^2 z^2 + y z^3 + z^4=0$
$ C^{A,C}_{123}$ $ x^3 z - x^2 y^2 + x^2 z^2 - x y^3 - 2 x y^2 z + x z^3 - y^4 - y^3 z - y^2 z^2=0$
$ C^A_{127}$ $ x^3 z - x^2 y^2 - 3 x^2 z^2 + x y^3 - x y z^2 + 4 x z^3 + 2 y^3 z - 3 y^2 z^2 + 3 y z^3 - 2 z^4=0$
$ C^B_{139}$ $ x^3 z - x^2 y^2 - 2 x^2 z^2 + x y^3 - 2 x y^2 z + 2 x y z^2 + x z^3 + y^4 -2 y^3 z + 4 y^2 z^2 - 3 y z^3=0$
$ C^{A,C,D}_{141}$ $ x^3 z - x^2 y^2 + x^2 z^2 - x y^3 + x y^2 z + x z^3 - y^4 - y^3 z - y^2 z^2=0$
$ C^A_{149}$ $ x^3 z - x^2 y^2 - 3 x^2 z^2 + x y^3 + 3 x y^2 z - 2 x y z^2 + 2 x z^3 - y^4 - y^2 z^2 + y z^3=0$
$ C^A_{151}$ $ x^3 z - 2 x^2 y z - 2 x^2 z^2 - x y^3 + 2 x y^2 z + 4 x y z^2 + x z^3 + y^2 z^2 - 3 y z^3 - 2 z^4=0$
$ C^B_{169}$ $ x^3 z - x^2 y^2 - 3 x^2 z^2 + x y^3 + 2 x y z^2 + x z^3 + y^2 z^2 - 3 y z^3 + z^4=0$
$ C^B_{179}$ $ x^3 z - 2 x^2 y z - 2 x^2 z^2 - x y^3 + 2 x y^2 z + x y z^2 + 2 x z^3 + y^2 z^2 - y z^3 - z^4=0$
$ C^E_{187}$ $ x^3 z - x^2 y^2 - x^2 z^2 + x y^3 - x y^2 z - x y z^2 + 2 x z^3 + y^3 z - y^2 z^2 + 3 y z^3=0$
$ C^F_{203}$ $ x^3 z - x^2 y^2 - 3 x^2 z^2 + x y^3 + 3 x y^2 z - 4 x y z^2 + 4 x z^3 - y^4 + 3 y^3 z - 6 y^2 z^2 + 3 y z^3 - 2 z^4=0$
$ C^A_{217}$ $ 3 x^3 z - 3 x^2 y^2 - 11 x^2 z^2 - 3 x y^3 + 13 x y^2 z - 2 x y z^2 + 11 x z^3 -2 y^4 - y^3 z - 4 y^2 z^2 + y z^3 - 2 z^4=0$
$ C^A_{239}$ $ x^3 z - x^2 y^2 - x^2 z^2 + x y^3 - x y^2 z + x z^3 + y^4 - y^3 z + y z^3 - z^4=0$
$ C^E_{243}$ $ x^3 z - 3 x^2 z^2 - x y^3 + 9 x y z^2 - 6 x z^3 + 2 y^3 z - 9 y^2 z^2 + 9 y z^3 - 2 z^4=0$
$ C^{A,D}_{243}$ $ x^3 z - x y^3 + 6 x z^3 - 4 y^3 z + 7 z^4 =0$
$ C^A_{295}$ $ x^3 z - x^2 y^2 - x^2 z^2 + x y^3 - x y^2 z + 2 x y z^2 - x z^3 - y^3 z + 3 y^2 z^2 - y z^3=0$
$ C^C_{329}$ $ x^3 z - x^2 y^2 + x y^3 + x y z^2 + x z^3 - y^3 z + 2 y z^3 + z^4 =0$
$ C^D_{369}$ $ x^3 z - 2 x^2 z^2 - x y^3 + 6 x y z^2 - 6 x z^3 - 3 y^2 z^2 + 6 y z^3 - z^4=0$
$ C^{B,I}_{459}$ $ x^3 z - x^2 z^2 - x y^3 + 5 x y z^2 - x z^3 + y^4 + 2 y^3 z - y^2 z^2 - 2 y z^3=0$
$ C^E_{475}$ $ x^3 z - x^2 y^2 - 5 x^2 z^2 - x y^3 + x y^2 z + 17 x y z^2 + 14 x z^3 - 2 y^4 - 14 y^3 z - 35 y^2 z^2 - 35 y z^3 - 12 z^4=0$
$ C^H_{855}$ $ x^3 z - x^2 z^2 - x y^3 + 3 x y z^2 - 3 x z^3 + 2 y^3 z - 3 y^2 z^2 + 3 y z^3=0$
$ C^D_{1175}$ $ x^3 z - x^2 y^2 + x^2 z^2 + x y^3 - 2 x y^2 z + 2 x y z^2 - x z^3 + y^4 - 2 y^3 z + y z^3=0$
$ C^P_{1215}$ $ x^3 z - x y^3 + 3 x y z^2 + 5 x z^3 - 6 y^2 z^2 - 3 y z^3 + z^4=0$
$ C^{A,K}_{1215}$ $ x^3 z - x y^3 + 3 x y z^2 + 5 x z^3 + 3 y^2 z^2 + 6 y z^3 - 8 z^4 =0$
$ C^{C,D,E}_{1539}$ $ x^3 z - 3 x^2 z^2 + 3 x y^2 z - 3 x y z^2 + 3 x z^3 - y^4 - 2 y^2 z^2 + y z^3 + 2 z^4=0$


- Case A: $ \, {\rm Jac}( {C} ) $is $ \mathbb{Q}$-simple. Then $ {\rm Jac}( {C} ) \Qisog A_f$, with $ f\in S_2(N,1)$ .
- Case AE: $ {\rm Jac}( {C} ) \stackrel{\mathbb{Q}}{\sim}E\times A$ , where $ E$ is an elliptic curve over $ \mathbb{Q}$ of conductor $ N$ and $ A$ is a $ \mathbb{Q}$ -simple abelian surface such that $ A_{f}\stackrel{\mathbb{Q}}{\sim}A$ where $ f\in S_2(N,\varepsilon)$ with $ ord (\varepsilon)\in\{1,2,3,4\}$ .
- Case EEE: $ {\rm Jac}( {C} ) \stackrel{\mathbb{Q}}{\sim}E_1\times E_2\times E_3$ , where $ E_1,E_2,E_3$ are elliptic curves defined over $ \mathbb{Q}$ of conductor $ N$ .

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