| 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 |
$abc$ quality |
Szpiro ratio |
Weierstrass coefficients |
Weierstrass equation |
mod-$m$ images |
MW-generators |
| 13454.a1 |
13454c1 |
13454.a |
13454c |
$1$ |
$1$ |
\( 2 \cdot 7 \cdot 31^{2} \) |
\( - 2^{13} \cdot 7^{3} \cdot 31^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$1736$ |
$2$ |
$0$ |
$0.608132306$ |
$1$ |
|
$4$ |
$9984$ |
$0.778006$ |
$529475129/2809856$ |
$0.95952$ |
$3.41746$ |
$[1, 1, 0, 523, 13357]$ |
\(y^2+xy=x^3+x^2+523x+13357\) |
1736.2.0.? |
$[(-3, 110)]$ |
| 13454.b1 |
13454a2 |
13454.b |
13454a |
$2$ |
$2$ |
\( 2 \cdot 7 \cdot 31^{2} \) |
\( 2^{3} \cdot 7^{2} \cdot 31^{8} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.6 |
2B |
$1736$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$46080$ |
$1.560741$ |
$11619959625/376712$ |
$1.00079$ |
$4.60500$ |
$[1, -1, 0, -45347, -3599891]$ |
\(y^2+xy=x^3-x^2-45347x-3599891\) |
2.3.0.a.1, 8.6.0.b.1, 868.6.0.?, 1736.12.0.? |
$[]$ |
| 13454.b2 |
13454a1 |
13454.b |
13454a |
$2$ |
$2$ |
\( 2 \cdot 7 \cdot 31^{2} \) |
\( 2^{6} \cdot 7 \cdot 31^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.1 |
2B |
$1736$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$23040$ |
$1.214169$ |
$41063625/13888$ |
$0.96508$ |
$4.01119$ |
$[1, -1, 0, -6907, 144165]$ |
\(y^2+xy=x^3-x^2-6907x+144165\) |
2.3.0.a.1, 8.6.0.c.1, 434.6.0.?, 1736.12.0.? |
$[]$ |
| 13454.c1 |
13454b1 |
13454.c |
13454b |
$1$ |
$1$ |
\( 2 \cdot 7 \cdot 31^{2} \) |
\( - 2^{13} \cdot 7^{3} \cdot 31^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$1736$ |
$2$ |
$0$ |
$7.759460671$ |
$1$ |
|
$0$ |
$309504$ |
$2.494999$ |
$529475129/2809856$ |
$0.95952$ |
$5.58469$ |
$[1, 0, 1, 502102, -391388900]$ |
\(y^2+xy+y=x^3+502102x-391388900\) |
1736.2.0.? |
$[(840544/33, 753633484/33)]$ |
| 13454.d1 |
13454d6 |
13454.d |
13454d |
$6$ |
$18$ |
\( 2 \cdot 7 \cdot 31^{2} \) |
\( 2^{9} \cdot 7^{2} \cdot 31^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.6, 9.12.0.1 |
2B, 3B |
$15624$ |
$864$ |
$21$ |
$5.480538865$ |
$1$ |
|
$0$ |
$181440$ |
$2.130096$ |
$2251439055699625/25088$ |
$1.06489$ |
$5.88557$ |
$[1, 1, 0, -2624030, 1634974964]$ |
\(y^2+xy=x^3+x^2-2624030x+1634974964\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.b.1, 9.12.0.a.1, $\ldots$ |
$[(92359/10, 132103/10)]$ |
| 13454.d2 |
13454d5 |
13454.d |
13454d |
$6$ |
$18$ |
\( 2 \cdot 7 \cdot 31^{2} \) |
\( - 2^{18} \cdot 7 \cdot 31^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.1, 9.12.0.1 |
2B, 3B |
$15624$ |
$864$ |
$21$ |
$10.96107773$ |
$1$ |
|
$1$ |
$90720$ |
$1.783522$ |
$-548347731625/1835008$ |
$1.02933$ |
$5.01101$ |
$[1, 1, 0, -163870, 25538292]$ |
\(y^2+xy=x^3+x^2-163870x+25538292\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.c.1, 9.12.0.a.1, $\ldots$ |
$[(2407788/103, 224425158/103)]$ |
| 13454.d3 |
13454d4 |
13454.d |
13454d |
$6$ |
$18$ |
\( 2 \cdot 7 \cdot 31^{2} \) |
\( 2^{3} \cdot 7^{6} \cdot 31^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.6, 3.12.0.1 |
2B, 3Cs |
$15624$ |
$864$ |
$21$ |
$1.826846288$ |
$1$ |
|
$2$ |
$60480$ |
$1.580788$ |
$4956477625/941192$ |
$1.00821$ |
$4.51538$ |
$[1, 1, 0, -34135, 1975533]$ |
\(y^2+xy=x^3+x^2-34135x+1975533\) |
2.3.0.a.1, 3.12.0.a.1, 6.36.0.a.1, 8.6.0.b.1, 24.72.1.h.1, $\ldots$ |
$[(-3, 1443)]$ |
| 13454.d4 |
13454d2 |
13454.d |
13454d |
$6$ |
$18$ |
\( 2 \cdot 7 \cdot 31^{2} \) |
\( 2 \cdot 7^{2} \cdot 31^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.6, 9.12.0.1 |
2B, 3B |
$15624$ |
$864$ |
$21$ |
$5.480538865$ |
$1$ |
|
$0$ |
$20160$ |
$1.031483$ |
$128787625/98$ |
$0.96763$ |
$4.13143$ |
$[1, 1, 0, -10110, -395254]$ |
\(y^2+xy=x^3+x^2-10110x-395254\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.b.1, 9.12.0.a.1, $\ldots$ |
$[(14947/9, 1402588/9)]$ |
| 13454.d5 |
13454d1 |
13454.d |
13454d |
$6$ |
$18$ |
\( 2 \cdot 7 \cdot 31^{2} \) |
\( - 2^{2} \cdot 7 \cdot 31^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.1, 9.12.0.1 |
2B, 3B |
$15624$ |
$864$ |
$21$ |
$10.96107773$ |
$1$ |
|
$1$ |
$10080$ |
$0.684909$ |
$-15625/28$ |
$1.01712$ |
$3.33129$ |
$[1, 1, 0, -500, -8932]$ |
\(y^2+xy=x^3+x^2-500x-8932\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.c.1, 9.12.0.a.1, $\ldots$ |
$[(73294/23, 18796640/23)]$ |
| 13454.d6 |
13454d3 |
13454.d |
13454d |
$6$ |
$18$ |
\( 2 \cdot 7 \cdot 31^{2} \) |
\( - 2^{6} \cdot 7^{3} \cdot 31^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.1, 3.12.0.1 |
2B, 3Cs |
$15624$ |
$864$ |
$21$ |
$3.653692576$ |
$1$ |
|
$3$ |
$30240$ |
$1.234215$ |
$9938375/21952$ |
$0.98695$ |
$3.97090$ |
$[1, 1, 0, 4305, 184229]$ |
\(y^2+xy=x^3+x^2+4305x+184229\) |
2.3.0.a.1, 3.12.0.a.1, 6.36.0.a.1, 8.6.0.c.1, 14.6.0.b.1, $\ldots$ |
$[(38, 617)]$ |
| 13454.e1 |
13454e2 |
13454.e |
13454e |
$2$ |
$2$ |
\( 2 \cdot 7 \cdot 31^{2} \) |
\( 2 \cdot 7^{2} \cdot 31^{8} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.6 |
2B |
$248$ |
$12$ |
$0$ |
$15.86376395$ |
$1$ |
|
$0$ |
$153600$ |
$1.859808$ |
$15732118860193/94178$ |
$0.93515$ |
$5.36347$ |
$[1, 0, 0, -501662, -136802942]$ |
\(y^2+xy=x^3-501662x-136802942\) |
2.3.0.a.1, 8.6.0.b.1, 124.6.0.?, 248.12.0.? |
$[(1171920687/638, 38394956973707/638)]$ |
| 13454.e2 |
13454e1 |
13454.e |
13454e |
$2$ |
$2$ |
\( 2 \cdot 7 \cdot 31^{2} \) |
\( - 2^{2} \cdot 7^{4} \cdot 31^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.1 |
2B |
$248$ |
$12$ |
$0$ |
$7.931881975$ |
$1$ |
|
$1$ |
$76800$ |
$1.513235$ |
$-3630961153/297724$ |
$0.86566$ |
$4.49659$ |
$[1, 0, 0, -30772, -2222580]$ |
\(y^2+xy=x^3-30772x-2222580\) |
2.3.0.a.1, 8.6.0.c.1, 62.6.0.b.1, 248.12.0.? |
$[(201572/29, 46972326/29)]$ |
| 13454.f1 |
13454g3 |
13454.f |
13454g |
$3$ |
$9$ |
\( 2 \cdot 7 \cdot 31^{2} \) |
\( - 2 \cdot 7^{9} \cdot 31^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.12.0.1 |
3B |
$15624$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$0$ |
$414720$ |
$2.465145$ |
$-4247828669470177/2501923634$ |
$0.96842$ |
$5.95245$ |
$[1, 1, 1, -3242434, 2247060129]$ |
\(y^2+xy+y=x^3+x^2-3242434x+2247060129\) |
3.4.0.a.1, 9.12.0.a.1, 93.8.0.?, 168.8.0.?, 279.72.0.?, $\ldots$ |
$[]$ |
| 13454.f2 |
13454g1 |
13454.f |
13454g |
$3$ |
$9$ |
\( 2 \cdot 7 \cdot 31^{2} \) |
\( - 2^{9} \cdot 7 \cdot 31^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.12.0.1 |
3B |
$15624$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$0$ |
$46080$ |
$1.366533$ |
$-7189057/111104$ |
$0.86905$ |
$4.17729$ |
$[1, 1, 1, -3864, -488231]$ |
\(y^2+xy+y=x^3+x^2-3864x-488231\) |
3.4.0.a.1, 9.12.0.a.1, 93.8.0.?, 168.8.0.?, 279.72.0.?, $\ldots$ |
$[]$ |
| 13454.f3 |
13454g2 |
13454.f |
13454g |
$3$ |
$9$ |
\( 2 \cdot 7 \cdot 31^{2} \) |
\( - 2^{3} \cdot 7^{3} \cdot 31^{9} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.12.0.1 |
3Cs |
$15624$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$0$ |
$138240$ |
$1.915838$ |
$5150827583/81746504$ |
$1.03194$ |
$4.86383$ |
$[1, 1, 1, 34576, 12735129]$ |
\(y^2+xy+y=x^3+x^2+34576x+12735129\) |
3.12.0.a.1, 93.24.0.?, 168.24.0.?, 279.72.0.?, 1736.2.0.?, $\ldots$ |
$[]$ |
| 13454.g1 |
13454h2 |
13454.g |
13454h |
$2$ |
$2$ |
\( 2 \cdot 7 \cdot 31^{2} \) |
\( 2^{5} \cdot 7^{4} \cdot 31^{8} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.6 |
2B |
$248$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$153600$ |
$1.937014$ |
$297141543217/73835552$ |
$0.91392$ |
$4.94596$ |
$[1, 1, 1, -133599, -14253595]$ |
\(y^2+xy+y=x^3+x^2-133599x-14253595\) |
2.3.0.a.1, 8.6.0.b.1, 124.6.0.?, 248.12.0.? |
$[]$ |
| 13454.g2 |
13454h1 |
13454.g |
13454h |
$2$ |
$2$ |
\( 2 \cdot 7 \cdot 31^{2} \) |
\( - 2^{10} \cdot 7^{2} \cdot 31^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.1 |
2B |
$248$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$76800$ |
$1.590439$ |
$1021147343/1555456$ |
$0.94016$ |
$4.40075$ |
$[1, 1, 1, 20161, -1399259]$ |
\(y^2+xy+y=x^3+x^2+20161x-1399259\) |
2.3.0.a.1, 8.6.0.c.1, 62.6.0.b.1, 248.12.0.? |
$[]$ |
| 13454.h1 |
13454f1 |
13454.h |
13454f |
$1$ |
$1$ |
\( 2 \cdot 7 \cdot 31^{2} \) |
\( - 2^{3} \cdot 7 \cdot 31^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$1736$ |
$2$ |
$0$ |
$1.456317339$ |
$1$ |
|
$0$ |
$460800$ |
$2.051517$ |
$-1460474194254993/1736$ |
$0.99205$ |
$5.84004$ |
$[1, -1, 1, -2271504, 1318273147]$ |
\(y^2+xy+y=x^3-x^2-2271504x+1318273147\) |
1736.2.0.? |
$[(7915/3, 607/3)]$ |
