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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