Some interesting modular curves

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
12.12.1-6.a.1.3	Parametrizes elliptic curves whose discriminant is a 12th power
13.78.3.a.1	$X_{\mathrm{ns}}^+(13)$, has a non-modular isomorphism to $X_{\mathrm{sp}}^+(13)$
13.91.3.b.1	$X_{\mathrm{sp}}^+(13)$, has a non-modular isomorphism to $X_{\mathrm{ns}}^+(13)$
13.168.2-13.b.2.2	$X_1(13)$, one of the three $X_1(N)$ of genus $2$
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 $\mathbb Q$.