| Label |
Description |
| 1.1.0.a.1 |
$X(1)$, the first modular curve |
| 2.6.0.a.1 |
$X(2)$, parameterizes twists of Legendre elliptic curves |
| 4.12.0-2.a.1.1 |
Parameterizes Legendre elliptic curves |
| 4.16.0-4.b.1.1 |
Parameterizes elliptic curves with same $2$- and $4$-division fields |
| 4.24.0-4.b.1.3 |
$X_1(2,4)$ |
| 5.120.0-5.a.1.2 |
$X_{\mathrm{arith}}(5)$, studied by Klein, icosahedral symmetry |
| 6.48.0-6.a.1.1 |
$X_1(2,6)$ |
| 7.336.3-7.b.1.2 |
$X_{\textup{arith}}(7)$, isomorphic to the Klein quartic |
| 8.12.1.c.1 |
A modular curve that is a rational point on itself |
| 8.12.1.d.1 |
A modular curve that is a rational point on itself |
| 8.96.0-8.l.2.2 |
$X_1(2,8)$, parametrizes elliptic curves with largest possible torsion subgroup |
| 8.384.5-8.d.1.1 |
$X_{\textup{arith}}(8)$, isomorphic to the Wiman curve |
| 11.12.1.a.1 |
$X_0(11)$, the first $X_0(N)$ of positive genus |
| 11.55.1.b.1 |
$X_{\textup{ns}}^+(11)$, the first positive rank modular curve |
| 11.120.1-11.a.2.2 |
$X_1(11)$, the first $X_1(N)$ of positive genus |
| 13.78.3.a.1 |
$X_{\mathrm{ns}}^+(13)$, has a non-modular isomorphism to $X_{\mathrm{sp}}^+(13)$ |
| 13.168.2-13.b.2.2 |
$X_1(13)$, one of the three $X_1(N)$ of genus $2$ |
| 13.91.3.b.1 |
$X_{\mathrm{sp}}^+(13)$, has a non-modular isomorphism to $X_{\mathrm{ns}}^+(13)$ |
| 15.24.1.a.1 |
$X_0(15)$, used in proof of Fermat's Last Theorem |
| 15.192.1-15.b.2.4 |
$X_1(15)$, the last $X_1(N)$ of genus $1$ |
| 16.24.1.n.2 |
Infinitely many rational points, but none with 2-adic image of index 24 |
| 16.192.2-16.l.1.1 |
$X_1(16)$, one of the three $X_1(N)$ of genus $2$ |
| 18.216.2-18.d.1.1 |
$X_1(18)$, one of the three $X_1(N)$ of genus $2$ |
| 21.384.5-21.c.1.4 |
$X_1(21)$, has a sporadic degree $3$ point |
| 25.150.4.b.1 |
A genus 4 curve whose Jacobian has a rational point of order 71 |
| 27.36.1.a.1 |
$X_0(27)$, isomorphic to the Fermat cubic |
| 34.54.3.a.1 |
$X_0(34)$, the first $X_0(N)$ of gonality 3 |
| 36.72.1.c.1 |
$X_0(36)$, a.k.a. $y^2=x^3+1$ |
| 37.38.2.a.1 |
$X_0(37)$ |
| 38.60.4.a.1 |
$X_0(38)$, the first $X_0(N)$ of gonality 4 |
| 48.144.11.t.1 |
A genus 11 hyperelliptic curve: $y^{2} = x^{24} + 64$. |
| 49.56.1.a.1 |
$X_0(49)$ |
| 60.540.38.bi.1 |
First known curve of genus 38 whose Jacobian is isogenous to a product of elliptic curves |
| 64.96.3.b.1 |
$X_0(64)$, isomorphic to the Fermat quartic |
| 109.110.8.a.1 |
$X_0(109)$, the only $X_0(N)$ of gonality 5 over $\mathbb Q$. |
