Modular curves over $\Q$

The database currently contains 16,835,992 modular curves of level $N\le 335$ parameterizing elliptic curves $E$ over $\Q$. You can browse further statistics.

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By family: $X_0(N)$  $X_1(N)$  $X(N)$  $X_{\mathrm{sp}}(N)$  $X_{\mathrm{sp}}^+(N)$  $X_{\mathrm{ns}}(N)$  $X_{\mathrm{ns}}^+(N)$  $X_{S_4}(p)$  $X_{\mathrm{arith}}(N)$ 

By level: prime  prime power  squarefree  1-4  5-8  9-12  13-16  17-23  24- 

By genus: 0  1  2  3  4-6  7-20  21-100  101- 

By rank: 0  1  2  3  4-6  7-20  21-100  101- 

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Level		e.g. 2, 11-23	Index		e.g. 6, 12-100
Genus		e.g. 0, 2-3	Rank		e.g. 0, 2-3
Genus-rank difference		e.g. 0, 1	$\Q$-gonality		e.g. 2, 3-6
Cusps		e.g. 1, 4-8	$\Q$-cusps		e.g. 0, 4-8
Elliptic points of order 2		e.g. 1,3-5	Elliptic points of order 3		e.g. 1,3-5
Simple			Squarefree
CM points		e.g. yes, no, CM discriminant -3	Fiber product with		e.g. 3.4.0.a.1
Minimally covers		e.g. 1.1.0.a.1	Minimally covered by		e.g. 6.12.0.a.1
Contains $-I$			Family		e.g. X0(N), Xsp(N)
Points		e.g. 0, 3-5	Obstructions
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Label or name
	e.g. 13.78.3.a.1, 13.78.3.a, 13.78.3.1, XNS+(13), 13Nn, 13A3, or X0(3)*X1(5) (fiber product over $X(1)$)