Label |
Cremona label |
Class |
Cremona class |
Class size |
Class degree |
Conductor |
Discriminant |
Rank |
Torsion |
$\textrm{End}^0(E_{\overline\Q})$ |
CM |
Sato-Tate |
Semistable |
Potentially good |
Nonmax $\ell$ |
$\ell$-adic images |
mod-$\ell$ images |
Adelic level |
Adelic index |
Adelic genus |
Regulator |
$Ш_{\textrm{an}}$ |
Ш primes |
Integral points |
Modular degree |
Faltings height |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
mod-$m$ images |
MW-generators |
714.a1 |
714d2 |
714.a |
714d |
$2$ |
$2$ |
\( 2 \cdot 3 \cdot 7 \cdot 17 \) |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 17^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.6.0.6 |
2B |
$952$ |
$12$ |
$0$ |
$0.259905232$ |
$1$ |
|
$10$ |
$192$ |
$0.160903$ |
$6141556990297/1019592$ |
$[1, 1, 0, -381, 2709]$ |
\(y^2+xy=x^3+x^2-381x+2709\) |
2.3.0.a.1, 8.6.0.b.1, 476.6.0.?, 952.12.0.? |
$[(9, 6)]$ |
714.a2 |
714d1 |
714.a |
714d |
$2$ |
$2$ |
\( 2 \cdot 3 \cdot 7 \cdot 17 \) |
\( - 2^{6} \cdot 3^{4} \cdot 7 \cdot 17 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.6.0.1 |
2B |
$952$ |
$12$ |
$0$ |
$0.519810465$ |
$1$ |
|
$9$ |
$96$ |
$-0.185670$ |
$-1102302937/616896$ |
$[1, 1, 0, -21, 45]$ |
\(y^2+xy=x^3+x^2-21x+45\) |
2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.? |
$[(2, 3)]$ |
714.b1 |
714b1 |
714.b |
714b |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 7 \cdot 17 \) |
\( - 2^{3} \cdot 3^{5} \cdot 7 \cdot 17 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$2856$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$120$ |
$-0.202091$ |
$-5841725401/231336$ |
$[1, 1, 0, -37, -107]$ |
\(y^2+xy=x^3+x^2-37x-107\) |
2856.2.0.? |
$[]$ |
714.c1 |
714c1 |
714.c |
714c |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 7 \cdot 17 \) |
\( - 2^{17} \cdot 3^{3} \cdot 7^{5} \cdot 17 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$2856$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$2040$ |
$1.173836$ |
$-344002044213921241/1011143540736$ |
$[1, 1, 0, -14597, -686643]$ |
\(y^2+xy=x^3+x^2-14597x-686643\) |
2856.2.0.? |
$[]$ |
714.d1 |
714a2 |
714.d |
714a |
$2$ |
$2$ |
\( 2 \cdot 3 \cdot 7 \cdot 17 \) |
\( 2^{7} \cdot 3^{4} \cdot 7^{6} \cdot 17^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.6.0.6 |
2B |
$952$ |
$12$ |
$0$ |
$0.887250634$ |
$1$ |
|
$6$ |
$2688$ |
$1.339388$ |
$18575453384550358633/352517816448$ |
$[1, 1, 0, -55174, 4965268]$ |
\(y^2+xy=x^3+x^2-55174x+4965268\) |
2.3.0.a.1, 8.6.0.b.1, 476.6.0.?, 952.12.0.? |
$[(139, 7)]$ |
714.d2 |
714a1 |
714.d |
714a |
$2$ |
$2$ |
\( 2 \cdot 3 \cdot 7 \cdot 17 \) |
\( - 2^{14} \cdot 3^{8} \cdot 7^{3} \cdot 17 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.6.0.1 |
2B |
$952$ |
$12$ |
$0$ |
$1.774501269$ |
$1$ |
|
$5$ |
$1344$ |
$0.992814$ |
$-4100379159705193/626805817344$ |
$[1, 1, 0, -3334, 81940]$ |
\(y^2+xy=x^3+x^2-3334x+81940\) |
2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.? |
$[(13, 196)]$ |
714.e1 |
714f4 |
714.e |
714f |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 7 \cdot 17 \) |
\( 2^{3} \cdot 3^{8} \cdot 7 \cdot 17 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.24.0.103 |
2B |
$952$ |
$48$ |
$0$ |
$0.845797302$ |
$1$ |
|
$4$ |
$768$ |
$0.646550$ |
$14489843500598257/6246072$ |
$[1, 1, 1, -5079, 137205]$ |
\(y^2+xy+y=x^3+x^2-5079x+137205\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.p.1.7, 476.12.0.?, 952.48.0.? |
$[(41, -18)]$ |
714.e2 |
714f3 |
714.e |
714f |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 7 \cdot 17 \) |
\( 2^{3} \cdot 3^{2} \cdot 7^{4} \cdot 17^{4} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.24.0.58 |
2B |
$952$ |
$48$ |
$0$ |
$0.211449325$ |
$1$ |
|
$10$ |
$768$ |
$0.646550$ |
$34623662831857/14438442312$ |
$[1, 1, 1, -679, -3883]$ |
\(y^2+xy+y=x^3+x^2-679x-3883\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.k.1.1, 952.48.0.? |
$[(-19, 60)]$ |
714.e3 |
714f2 |
714.e |
714f |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 7 \cdot 17 \) |
\( 2^{6} \cdot 3^{4} \cdot 7^{2} \cdot 17^{2} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.24.0.1 |
2Cs |
$952$ |
$48$ |
$0$ |
$0.422898651$ |
$1$ |
|
$16$ |
$384$ |
$0.299976$ |
$3590714269297/73410624$ |
$[1, 1, 1, -319, 2021]$ |
\(y^2+xy+y=x^3+x^2-319x+2021\) |
2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.a.1.2, 476.24.0.?, 952.48.0.? |
$[(7, 10)]$ |
714.e4 |
714f1 |
714.e |
714f |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 7 \cdot 17 \) |
\( - 2^{12} \cdot 3^{2} \cdot 7 \cdot 17 \) |
$1$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.24.0.50 |
2B |
$952$ |
$48$ |
$0$ |
$0.845797302$ |
$1$ |
|
$13$ |
$192$ |
$-0.046597$ |
$103823/4386816$ |
$[1, 1, 1, 1, 101]$ |
\(y^2+xy+y=x^3+x^2+x+101\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.p.1.1, 238.6.0.?, 476.24.0.?, $\ldots$ |
$[(-3, 10)]$ |
714.f1 |
714g5 |
714.f |
714g |
$6$ |
$8$ |
\( 2 \cdot 3 \cdot 7 \cdot 17 \) |
\( 2^{3} \cdot 3^{8} \cdot 7^{2} \cdot 17^{8} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.96.0.164 |
2B |
$272$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$30720$ |
$2.579128$ |
$285531136548675601769470657/17941034271597192$ |
$[1, 1, 1, -13718604, -19563199515]$ |
\(y^2+xy+y=x^3+x^2-13718604x-19563199515\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.96.0-8.p.1.4, 272.192.1.? |
$[]$ |
714.f2 |
714g3 |
714.f |
714g |
$6$ |
$8$ |
\( 2 \cdot 3 \cdot 7 \cdot 17 \) |
\( 2^{6} \cdot 3^{16} \cdot 7^{4} \cdot 17^{4} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.96.0.50 |
2Cs |
$136$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$2$ |
$15360$ |
$2.232555$ |
$70108386184777836280897/552468975892674624$ |
$[1, 1, 1, -859044, -304722459]$ |
\(y^2+xy+y=x^3+x^2-859044x-304722459\) |
2.6.0.a.1, 4.24.0-4.b.1.1, 8.96.0-8.f.1.1, 136.192.1.? |
$[]$ |
714.f3 |
714g6 |
714.f |
714g |
$6$ |
$8$ |
\( 2 \cdot 3 \cdot 7 \cdot 17 \) |
\( - 2^{3} \cdot 3^{32} \cdot 7^{2} \cdot 17^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
16.96.0.137 |
2B |
$272$ |
$192$ |
$1$ |
$1$ |
$4$ |
$2$ |
$0$ |
$30720$ |
$2.579128$ |
$-2770540998624539614657/209924951154647363208$ |
$[1, 1, 1, -292604, -699871003]$ |
\(y^2+xy+y=x^3+x^2-292604x-699871003\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.k.1.6, 16.96.0-16.e.1.6, 136.96.0.?, $\ldots$ |
$[]$ |
714.f4 |
714g2 |
714.f |
714g |
$6$ |
$8$ |
\( 2 \cdot 3 \cdot 7 \cdot 17 \) |
\( 2^{12} \cdot 3^{8} \cdot 7^{8} \cdot 17^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.96.0.37 |
2Cs |
$136$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$6$ |
$7680$ |
$1.885983$ |
$82582985847542515777/44772582831427584$ |
$[1, 1, 1, -90724, 2605541]$ |
\(y^2+xy+y=x^3+x^2-90724x+2605541\) |
2.6.0.a.1, 4.24.0-4.b.1.3, 8.96.0-8.i.1.2, 68.48.0-68.c.1.1, 136.192.1.? |
$[]$ |
714.f5 |
714g1 |
714.f |
714g |
$6$ |
$8$ |
\( 2 \cdot 3 \cdot 7 \cdot 17 \) |
\( 2^{24} \cdot 3^{4} \cdot 7^{4} \cdot 17 \) |
$0$ |
$\Z/8\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
16.96.0.98 |
2B |
$272$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$7$ |
$3840$ |
$1.539408$ |
$38331145780597164097/55468445663232$ |
$[1, 1, 1, -70244, 7127525]$ |
\(y^2+xy+y=x^3+x^2-70244x+7127525\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.48.0-8.bb.1.1, 16.96.0-16.z.1.2, 34.6.0.a.1, $\ldots$ |
$[]$ |
714.f6 |
714g4 |
714.f |
714g |
$6$ |
$8$ |
\( 2 \cdot 3 \cdot 7 \cdot 17 \) |
\( - 2^{6} \cdot 3^{4} \cdot 7^{16} \cdot 17 \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
16.96.0.103 |
2B |
$272$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$2$ |
$15360$ |
$2.232555$ |
$4738217997934888496063/2928751705237796928$ |
$[1, 1, 1, 349916, 20936165]$ |
\(y^2+xy+y=x^3+x^2+349916x+20936165\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.48.0-8.bb.2.4, 16.96.0-16.z.2.3, 68.24.0-68.h.1.2, $\ldots$ |
$[]$ |
714.g1 |
714e1 |
714.g |
714e |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 7 \cdot 17 \) |
\( - 2^{7} \cdot 3^{3} \cdot 7 \cdot 17^{5} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$2856$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$840$ |
$0.800868$ |
$-1184052061112257/34349180544$ |
$[1, 1, 1, -2204, -41731]$ |
\(y^2+xy+y=x^3+x^2-2204x-41731\) |
2856.2.0.? |
$[]$ |
714.h1 |
714h1 |
714.h |
714h |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 7 \cdot 17 \) |
\( - 2 \cdot 3 \cdot 7 \cdot 17 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$2856$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$40$ |
$-0.770755$ |
$103823/714$ |
$[1, 1, 1, 1, -1]$ |
\(y^2+xy+y=x^3+x^2+x-1\) |
2856.2.0.? |
$[]$ |
714.i1 |
714i3 |
714.i |
714i |
$3$ |
$9$ |
\( 2 \cdot 3 \cdot 7 \cdot 17 \) |
\( - 2 \cdot 3 \cdot 7^{3} \cdot 17^{9} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
9.72.0.12 |
3B.1.2 |
$8568$ |
$144$ |
$3$ |
$1$ |
$9$ |
$3$ |
$0$ |
$9720$ |
$1.844110$ |
$-6150311179917589675873/244053849830826$ |
$[1, 0, 0, -381702, -90803346]$ |
\(y^2+xy=x^3-381702x-90803346\) |
3.8.0-3.a.1.1, 9.72.0-9.d.2.2, 2856.16.0.?, 8568.144.3.? |
$[]$ |
714.i2 |
714i2 |
714.i |
714i |
$3$ |
$9$ |
\( 2 \cdot 3 \cdot 7 \cdot 17 \) |
\( - 2^{3} \cdot 3^{3} \cdot 7^{9} \cdot 17^{3} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
9.72.0.1 |
3Cs.1.1 |
$8568$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$2$ |
$3240$ |
$1.294804$ |
$-101566487155393/42823570577256$ |
$[1, 0, 0, -972, -315144]$ |
\(y^2+xy=x^3-972x-315144\) |
3.24.0-3.a.1.1, 9.72.0-9.a.1.1, 2856.48.1.?, 8568.144.3.? |
$[]$ |
714.i3 |
714i1 |
714.i |
714i |
$3$ |
$9$ |
\( 2 \cdot 3 \cdot 7 \cdot 17 \) |
\( - 2^{9} \cdot 3^{9} \cdot 7^{3} \cdot 17 \) |
$0$ |
$\Z/9\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
9.72.0.5 |
3B.1.1 |
$8568$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$8$ |
$1080$ |
$0.745499$ |
$139233463487/58763045376$ |
$[1, 0, 0, 108, 11664]$ |
\(y^2+xy=x^3+108x+11664\) |
3.8.0-3.a.1.2, 9.72.0-9.d.1.2, 2856.16.0.?, 8568.144.3.? |
$[]$ |