| Label |
Description |
| 11.a1 |
First curve with trivial Mordell-Weil group |
| 11.a2 |
Modular curve $X_0(11)$ |
| 11.a3 |
Modular curve $X_1(11)$ |
| 14.a5 |
Modular curve $X_1(14)$ |
| 14.a6 |
Modular curve $X_0(14)$ |
| 15.a2 |
Frey curve for $1+80=81$ |
| 15.a5 |
Modular curve $X_0(15)$ |
| 15.a7 |
Modular curve $X_1(15)$ |
| 17.a3 |
Modular curve $X_0(17)$ |
| 19.a2 |
Modular curve $X_0(19)$ |
| 20.a4 |
Modular curve $X_0(20)$ |
| 21.a5 |
Modular curve $X_0(21)$ |
| 24.a4 |
Modular curve $X_0(24)$ |
| 27.a3 |
Modular curve $X_0(27)$ |
| 27.a4 |
Model for $XY(X+Y)=Z^3$ |
| 30.a3 |
Frey curve for $3+125=128$ |
| 30.a6 |
First curve with torsion $\Z/2\Z \times \Z/6\Z$ |
| 32.a4 |
Modular curve $X_0(32)$ |
| 36.a4 |
Modular curve $X_0(36)$ |
| 37.a1 |
First rank-1 curve; modular curve $X_0(37)/ \langle w_{37} \rangle = X_0^+(37)$ |
| 37.b2 |
Last prime-power discriminant $\pm N^e$ with $e>2$ |
| 37.b3 |
Minimal twist of original curve used for class number problem |
| 43.a1 |
Modular curve $X_0(43)/ \langle w_{43} \rangle = X_0^+(43)$ |
| 49.a2 |
Quotient of the degree-7 Fermat curve |
| 49.a4 |
Modular curve $X_0(49)$ |
| 50.a3 |
Quotient of Bring's curve by a simple transposition in $S_5$ |
| 52.a1 |
First example of a congruence mod 13 |
| 53.a1 |
Modular curve $X_0(53)/ \langle w_{53} \rangle = X_0^+(53)$ |
| 57.a1 |
Modular curve $X_0(57) / \langle w_3, w_{19} \rangle$ |
| 58.a1 |
Modular curve $X_0(58) / \langle w_2, w_{29} \rangle$ |
| 61.a1 |
Modular curve $X_0(61)/\langle w_{61} \rangle = X_0^+(61)$ |
| 65.a1 |
Modular curve $X_0(65)/ \langle w_{65} \rangle = X_0^+(65)$ |
| 65.a2 |
Modular curve $X_0(65) / \langle w_5, w_{13} \rangle$ |
| 66.c4 |
Elliptic curve 66.c4 and 70-torsion of a genus-2 Jacobian |
| 77.a1 |
Modular curve $X_0(77) / \langle w_7, w_{11} \rangle$ |
| 79.a1 |
Modular curve $X_0(79)/ \langle w_{79} \rangle = X_0^+(79)$ |
| 83.a1 |
Modular curve $X_0(83)/ \langle w_{83} \rangle = X_0^+(83)$ |
| 88.a1 |
Richard Guy's "favorite elliptic curve" |
| 91.a1 |
Modular curve $X_0(91) / \langle w_7, w_{13} \rangle$ |
| 101.a1 |
Modular curve $X_0(101)/\langle w_{101} \rangle = X_0^+(101)$ |
| 102.a1 |
Elliptic Curve 102.a1 and Somos-5 Sequene |
| 118.a1 |
Modular curve $X_0(118) / \langle w_2, w_{59} \rangle$ |
| 121.b2 |
Modular curve $X_{\text{ns}}^{+}(11)$ |
| 123.b1 |
Modular curve $X_0(123) / \langle w_3, w_{41} \rangle$ |
| 131.a1 |
Modular curve $X_0(131)/ \langle w_{131} \rangle = X_0^+(131)$ |
| 141.d1 |
Modular curve $X_0(141) / \langle w_3, w_{47} \rangle$ |
| 142.a1 |
Modular curve $X_0(142) / \langle w_2, w_{71} \rangle$ |
| 143.a1 |
Modular curve $X_0(143) / \langle w_{11}, w_{13} \rangle$ |
| 155.c1 |
Modular curve $X_0(155) / \langle w_5, w_{31} \rangle$ |
| 162.c3 |
Sporadic cubic point on $X_1(21)$ |
| 189.b1 |
First curve for which mod-p specialization is never surjective |
| 196.a2 |
Quotient of the Fricke-Macbeath curve |
| 210.e6 |
First curve with torsion $\Z/2\Z \times \Z/8\Z$ |
| 256.b1 |
Modular curve $X(16B^1$-$16c)$ |
| 389.a1 |
First elliptic curve of rank 2 |
| 400.a1 |
Elliptic curve whose modular parametrization has a multiple branch point |
| 858.k1 |
Elliptic curve 858.k1 and 70-torsion of a genus 2 Jacobian |
| 910.a4 |
'Fruits meme' elliptic curve |
| 988.c1 |
First example of a congruence modulo 13 |
| 1830.l1 |
Highest known integral multiple of a nontorsion point |
| 1944.e1 |
Surjective mod 3 but nonsurjective mod 9 |
| 2450.i1 |
Violation of local-global principle for isogenies |
| 3630.y1 |
Second-smallest known nontorsion point |
| 3675.g1 |
First mod-17 congruence |
| 3990.v1 |
Smallest known nonzero canonical height |
| 4650.f1 |
Example of a triple of 9-congruent elliptic curves |
| 5077.a1 |
The Gauss elliptic curve 5077a1 |
| 8604.a1 |
Diophantine realization |
| 21168.ce2 |
Curve secp256k1 in ECDSA specification |
| 27606.c1 |
Example of a triple of 9-congruent elliptic curves |
| 47775.be1 |
First mod-17 congruence |
| 47775.bn1 |
Example of a triple of 9-congruent elliptic curves |
| 220110.bn1 |
Smallest known nontorsion point on a curve of rank >1 |
| 234446.a1 |
First elliptic curve of rank 4 |
| 358878.n1 |
Example of a triple of 9-congruent elliptic curves |
| 147.b |
First isogeny class with a 13-isogeny |
| 147.c |
First isogeny class with a 13-isogeny |
