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 |
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 |