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 |
429.a1 |
429a2 |
429.a |
429a |
$2$ |
$2$ |
\( 3 \cdot 11 \cdot 13 \) |
\( 3 \cdot 11^{2} \cdot 13^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
2.3.0.1 |
2B |
$1716$ |
$12$ |
$0$ |
$0.349010001$ |
$1$ |
|
$8$ |
$32$ |
$-0.371365$ |
$244140625/61347$ |
$[1, 1, 1, -13, 8]$ |
\(y^2+xy+y=x^3+x^2-13x+8\) |
2.3.0.a.1, 12.6.0.a.1, 572.6.0.?, 1716.12.0.? |
$[(4, 4)]$ |
429.a2 |
429a1 |
429.a |
429a |
$2$ |
$2$ |
\( 3 \cdot 11 \cdot 13 \) |
\( - 3^{2} \cdot 11 \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
2.3.0.1 |
2B |
$1716$ |
$12$ |
$0$ |
$0.698020003$ |
$1$ |
|
$5$ |
$16$ |
$-0.717938$ |
$857375/1287$ |
$[1, 1, 1, 2, 2]$ |
\(y^2+xy+y=x^3+x^2+2x+2\) |
2.3.0.a.1, 12.6.0.b.1, 286.6.0.?, 1716.12.0.? |
$[(0, 1)]$ |
429.b1 |
429b4 |
429.b |
429b |
$6$ |
$8$ |
\( 3 \cdot 11 \cdot 13 \) |
\( 3^{2} \cdot 11 \cdot 13 \) |
$1$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.24.0.45 |
2B |
$6864$ |
$192$ |
$1$ |
$4.230906392$ |
$1$ |
|
$4$ |
$256$ |
$0.541096$ |
$35765103905346817/1287$ |
$[1, 0, 0, -6864, 218313]$ |
\(y^2+xy=x^3-6864x+218313\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 48.48.0-48.g.1.7, 176.48.0.?, $\ldots$ |
$[(104, 743)]$ |
429.b2 |
429b5 |
429.b |
429b |
$6$ |
$8$ |
\( 3 \cdot 11 \cdot 13 \) |
\( 3 \cdot 11^{8} \cdot 13^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.24.0.55 |
2B |
$6864$ |
$192$ |
$1$ |
$2.115453196$ |
$1$ |
|
$2$ |
$512$ |
$0.887670$ |
$3013001140430737/108679952667$ |
$[1, 0, 0, -3009, -61770]$ |
\(y^2+xy=x^3-3009x-61770\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 12.24.0-12.h.1.1, 24.48.0-24.bl.1.1, $\ldots$ |
$[(-34, 56)]$ |
429.b3 |
429b3 |
429.b |
429b |
$6$ |
$8$ |
\( 3 \cdot 11 \cdot 13 \) |
\( 3^{2} \cdot 11^{4} \cdot 13^{4} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
4.24.0.6 |
2Cs |
$3432$ |
$192$ |
$1$ |
$1.057726598$ |
$1$ |
|
$8$ |
$256$ |
$0.541096$ |
$11779205551777/3763454409$ |
$[1, 0, 0, -474, 2619]$ |
\(y^2+xy=x^3-474x+2619\) |
2.6.0.a.1, 4.24.0-4.b.1.1, 12.48.0-12.c.1.3, 88.48.0.?, 104.48.0.?, $\ldots$ |
$[(5, 17)]$ |
429.b4 |
429b2 |
429.b |
429b |
$6$ |
$8$ |
\( 3 \cdot 11 \cdot 13 \) |
\( 3^{4} \cdot 11^{2} \cdot 13^{2} \) |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
4.24.0.5 |
2Cs |
$3432$ |
$192$ |
$1$ |
$2.115453196$ |
$1$ |
|
$12$ |
$128$ |
$0.194522$ |
$8732907467857/1656369$ |
$[1, 0, 0, -429, 3384]$ |
\(y^2+xy=x^3-429x+3384\) |
2.6.0.a.1, 4.24.0-4.b.1.3, 24.48.0-24.m.1.6, 88.48.0.?, 104.48.0.?, $\ldots$ |
$[(24, 72)]$ |
429.b5 |
429b1 |
429.b |
429b |
$6$ |
$8$ |
\( 3 \cdot 11 \cdot 13 \) |
\( - 3^{8} \cdot 11 \cdot 13 \) |
$1$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.24.0.45 |
2B |
$6864$ |
$192$ |
$1$ |
$1.057726598$ |
$1$ |
|
$9$ |
$64$ |
$-0.152051$ |
$-1532808577/938223$ |
$[1, 0, 0, -24, 63]$ |
\(y^2+xy=x^3-24x+63\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 48.48.0-48.g.1.7, 88.48.0.?, $\ldots$ |
$[(6, 9)]$ |
429.b6 |
429b6 |
429.b |
429b |
$6$ |
$8$ |
\( 3 \cdot 11 \cdot 13 \) |
\( - 3 \cdot 11^{2} \cdot 13^{8} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.24.0.55 |
2B |
$6864$ |
$192$ |
$1$ |
$0.528863299$ |
$1$ |
|
$4$ |
$512$ |
$0.887670$ |
$266679605718863/296110251723$ |
$[1, 0, 0, 1341, 18228]$ |
\(y^2+xy=x^3+1341x+18228\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 6.6.0.a.1, 8.24.0-8.n.1.6, 12.24.0-12.g.1.1, $\ldots$ |
$[(17, 206)]$ |