Tables of New Modular Hyperelliptic Curves

Table	genus	Jacobian	$\char93 {\mathcal{D}}$	$N\leq$	$\char93$
	2	$\overline{\mathbb{Q}}$-simple	-	$\infty$	96
	2	$\mathbb{Q}$-simple	-	$\infty$	53
	2	No $\mathbb{Q}$-simple	-	$\infty$	64
	3	$\mathbb{Q}$-simple	1	3000*	14
	4	$\mathbb{Q}$-simple	1	3000*	13
	5	$\mathbb{Q}$-simple	1	3000*	3
	3	No $\mathbb{Q}$-simple	1	2000**	32
	4	No $\mathbb{Q}$-simple	1	2000**	7
	6	No $\mathbb{Q}$-simple	1	2000**	1
	3	-	3	$\infty$	5
	3 or 4	-	$2\mid \char93 {\mathcal{D}}$, $w\notin {\mathcal{D}}$	$\infty$	7
	$\geq$4	-	$>$1, otherwise	600	5

 

 

*   All the curves with genus > 2, ${\mathcal{D}}$> 1, jacobian $\mathbb{Q}$-simple and level $\leq$3000 have genus 3, 4 or 5.

 

** All the curves with genus > 2, ${\mathcal{D}}$> 1, jacobian No $\mathbb{Q}$-simple and level $\leq$2000 have genus 3, 4 or 6.

 

These tables appear in

• Enrique González-Jiménez and Josep González, "Modular curves of genus 2", Math. Comp. 72, no. 241, 397—418, (2003).
• Matthew H. Baker, Enrique González-Jiménez, Josep González and Bjorn Poonen, "Finitness results for modular curves of genus at least 2", Amer. J. Math. 127, no. 6, 1325-1387, (2005).