| 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 |
| 4719.a1 |
4719e1 |
4719.a |
4719e |
$1$ |
$1$ |
\( 3 \cdot 11^{2} \cdot 13 \) |
\( - 3^{5} \cdot 11^{10} \cdot 13^{4} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$84480$ |
$2.007957$ |
$-7744000000/6940323$ |
$1.07771$ |
$5.63692$ |
$[0, -1, 1, -122008, 26227860]$ |
\(y^2+y=x^3-x^2-122008x+26227860\) |
6.2.0.a.1 |
$[]$ |
| 4719.b1 |
4719k1 |
4719.b |
4719k |
$1$ |
$1$ |
\( 3 \cdot 11^{2} \cdot 13 \) |
\( - 3^{7} \cdot 11^{2} \cdot 13^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$0.063544874$ |
$1$ |
|
$12$ |
$3360$ |
$0.456522$ |
$-1518309117952/369603$ |
$0.97601$ |
$3.88266$ |
$[0, 1, 1, -1184, 15296]$ |
\(y^2+y=x^3+x^2-1184x+15296\) |
6.2.0.a.1 |
$[(22, 19)]$ |
| 4719.c1 |
4719d4 |
4719.c |
4719d |
$4$ |
$4$ |
\( 3 \cdot 11^{2} \cdot 13 \) |
\( 3^{4} \cdot 11^{6} \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$3432$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$5120$ |
$0.880581$ |
$37159393753/1053$ |
$1.11616$ |
$4.57787$ |
$[1, 1, 1, -8412, 293448]$ |
\(y^2+xy+y=x^3+x^2-8412x+293448\) |
2.3.0.a.1, 4.6.0.c.1, 24.12.0.ba.1, 26.6.0.b.1, 44.12.0-4.c.1.1, $\ldots$ |
$[]$ |
| 4719.c2 |
4719d3 |
4719.c |
4719d |
$4$ |
$4$ |
\( 3 \cdot 11^{2} \cdot 13 \) |
\( 3 \cdot 11^{6} \cdot 13^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$3432$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$5120$ |
$0.880581$ |
$822656953/85683$ |
$0.96086$ |
$4.12743$ |
$[1, 1, 1, -2362, -40996]$ |
\(y^2+xy+y=x^3+x^2-2362x-40996\) |
2.3.0.a.1, 4.6.0.c.1, 12.12.0.h.1, 44.12.0-4.c.1.2, 104.12.0.?, $\ldots$ |
$[]$ |
| 4719.c3 |
4719d2 |
4719.c |
4719d |
$4$ |
$4$ |
\( 3 \cdot 11^{2} \cdot 13 \) |
\( 3^{2} \cdot 11^{6} \cdot 13^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.6.0.1 |
2Cs |
$1716$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$2560$ |
$0.534008$ |
$10218313/1521$ |
$0.91403$ |
$3.60868$ |
$[1, 1, 1, -547, 4016]$ |
\(y^2+xy+y=x^3+x^2-547x+4016\) |
2.6.0.a.1, 12.12.0.a.1, 44.12.0-2.a.1.1, 52.12.0.b.1, 132.24.0.?, $\ldots$ |
$[]$ |
| 4719.c4 |
4719d1 |
4719.c |
4719d |
$4$ |
$4$ |
\( 3 \cdot 11^{2} \cdot 13 \) |
\( - 3 \cdot 11^{6} \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$3432$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$1280$ |
$0.187434$ |
$12167/39$ |
$0.85844$ |
$2.99155$ |
$[1, 1, 1, 58, 386]$ |
\(y^2+xy+y=x^3+x^2+58x+386\) |
2.3.0.a.1, 4.6.0.c.1, 24.12.0.ba.1, 78.6.0.?, 88.12.0.?, $\ldots$ |
$[]$ |
| 4719.d1 |
4719b1 |
4719.d |
4719b |
$1$ |
$1$ |
\( 3 \cdot 11^{2} \cdot 13 \) |
\( - 3^{9} \cdot 11^{4} \cdot 13^{2} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$31104$ |
$1.647549$ |
$-462482914449031168/3326427$ |
$1.11284$ |
$5.94218$ |
$[0, -1, 1, -394137, -95108641]$ |
\(y^2+y=x^3-x^2-394137x-95108641\) |
6.2.0.a.1 |
$[]$ |
| 4719.e1 |
4719f1 |
4719.e |
4719f |
$1$ |
$1$ |
\( 3 \cdot 11^{2} \cdot 13 \) |
\( - 3 \cdot 11^{2} \cdot 13^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$0.964613657$ |
$1$ |
|
$2$ |
$384$ |
$-0.389031$ |
$-360448/507$ |
$0.84429$ |
$2.22518$ |
$[0, -1, 1, -7, -12]$ |
\(y^2+y=x^3-x^2-7x-12\) |
6.2.0.a.1 |
$[(8, 19)]$ |
| 4719.f1 |
4719a1 |
4719.f |
4719a |
$1$ |
$1$ |
\( 3 \cdot 11^{2} \cdot 13 \) |
\( - 3 \cdot 11^{8} \cdot 13^{2} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$4224$ |
$0.809916$ |
$-360448/507$ |
$0.84429$ |
$3.92595$ |
$[0, -1, 1, -887, 19139]$ |
\(y^2+y=x^3-x^2-887x+19139\) |
6.2.0.a.1 |
$[]$ |
| 4719.g1 |
4719g1 |
4719.g |
4719g |
$1$ |
$1$ |
\( 3 \cdot 11^{2} \cdot 13 \) |
\( - 3^{9} \cdot 11^{10} \cdot 13^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$7.519269176$ |
$1$ |
|
$2$ |
$342144$ |
$2.846497$ |
$-462482914449031168/3326427$ |
$1.11284$ |
$7.64294$ |
$[0, -1, 1, -47690617, 126780363258]$ |
\(y^2+y=x^3-x^2-47690617x+126780363258\) |
6.2.0.a.1 |
$[(9308, 699445)]$ |
| 4719.h1 |
4719l1 |
4719.h |
4719l |
$2$ |
$3$ |
\( 3 \cdot 11^{2} \cdot 13 \) |
\( - 3^{3} \cdot 11^{8} \cdot 13^{2} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.1 |
3B.1.1 |
$6$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$5280$ |
$1.110514$ |
$-360448000/4563$ |
$0.96400$ |
$4.59937$ |
$[0, 1, 1, -8873, 322262]$ |
\(y^2+y=x^3+x^2-8873x+322262\) |
3.8.0-3.a.1.2, 6.16.0-6.b.1.2 |
$[]$ |
| 4719.h2 |
4719l2 |
4719.h |
4719l |
$2$ |
$3$ |
\( 3 \cdot 11^{2} \cdot 13 \) |
\( - 3 \cdot 11^{8} \cdot 13^{6} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.2 |
3B.1.2 |
$6$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$15840$ |
$1.659821$ |
$15454208000/14480427$ |
$1.00318$ |
$5.04108$ |
$[0, 1, 1, 31057, 1667903]$ |
\(y^2+y=x^3+x^2+31057x+1667903\) |
3.8.0-3.a.1.1, 6.16.0-6.b.1.1 |
$[]$ |
| 4719.i1 |
4719i1 |
4719.i |
4719i |
$2$ |
$3$ |
\( 3 \cdot 11^{2} \cdot 13 \) |
\( - 3^{3} \cdot 11^{2} \cdot 13^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$66$ |
$16$ |
$0$ |
$0.775615233$ |
$1$ |
|
$4$ |
$480$ |
$-0.088433$ |
$-360448000/4563$ |
$0.96400$ |
$2.89860$ |
$[0, 1, 1, -73, -269]$ |
\(y^2+y=x^3+x^2-73x-269\) |
3.4.0.a.1, 6.8.0.b.1, 33.8.0-3.a.1.2, 66.16.0-6.b.1.2 |
$[(11, 19)]$ |
| 4719.i2 |
4719i2 |
4719.i |
4719i |
$2$ |
$3$ |
\( 3 \cdot 11^{2} \cdot 13 \) |
\( - 3 \cdot 11^{2} \cdot 13^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$66$ |
$16$ |
$0$ |
$2.326845699$ |
$1$ |
|
$0$ |
$1440$ |
$0.460873$ |
$15454208000/14480427$ |
$1.00318$ |
$3.34032$ |
$[0, 1, 1, 257, -1160]$ |
\(y^2+y=x^3+x^2+257x-1160\) |
3.4.0.a.1, 6.8.0.b.1, 33.8.0-3.a.1.1, 66.16.0-6.b.1.1 |
$[(154/5, 3233/5)]$ |
| 4719.j1 |
4719c2 |
4719.j |
4719c |
$2$ |
$2$ |
\( 3 \cdot 11^{2} \cdot 13 \) |
\( 3 \cdot 11^{8} \cdot 13^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$1716$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$3840$ |
$0.827583$ |
$244140625/61347$ |
$1.08894$ |
$3.98383$ |
$[1, 1, 0, -1575, -18762]$ |
\(y^2+xy=x^3+x^2-1575x-18762\) |
2.3.0.a.1, 12.6.0.a.1, 572.6.0.?, 1716.12.0.? |
$[]$ |
| 4719.j2 |
4719c1 |
4719.j |
4719c |
$2$ |
$2$ |
\( 3 \cdot 11^{2} \cdot 13 \) |
\( - 3^{2} \cdot 11^{7} \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$1716$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$1920$ |
$0.481009$ |
$857375/1287$ |
$0.79548$ |
$3.37085$ |
$[1, 1, 0, 240, -1701]$ |
\(y^2+xy=x^3+x^2+240x-1701\) |
2.3.0.a.1, 12.6.0.b.1, 286.6.0.?, 1716.12.0.? |
$[]$ |
| 4719.k1 |
4719j3 |
4719.k |
4719j |
$6$ |
$8$ |
\( 3 \cdot 11^{2} \cdot 13 \) |
\( 3^{2} \cdot 11^{7} \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.24.0.3 |
2B |
$6864$ |
$192$ |
$1$ |
$14.99029441$ |
$1$ |
|
$0$ |
$30720$ |
$1.740044$ |
$35765103905346817/1287$ |
$0.98956$ |
$6.20652$ |
$[1, 0, 1, -830547, -291405149]$ |
\(y^2+xy+y=x^3-830547x-291405149\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0-8.n.1.5, 24.24.0-8.n.1.8, $\ldots$ |
$[(3837119/58, 2946422025/58)]$ |
| 4719.k2 |
4719j5 |
4719.k |
4719j |
$6$ |
$8$ |
\( 3 \cdot 11^{2} \cdot 13 \) |
\( 3 \cdot 11^{14} \cdot 13^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.24.0.14 |
2B |
$6864$ |
$192$ |
$1$ |
$7.495147205$ |
$1$ |
|
$0$ |
$61440$ |
$2.086617$ |
$3013001140430737/108679952667$ |
$0.97853$ |
$5.91406$ |
$[1, 0, 1, -364092, 81851779]$ |
\(y^2+xy+y=x^3-364092x+81851779\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 12.12.0.h.1, 16.24.0-8.n.1.6, $\ldots$ |
$[(-35567/9, 9297244/9)]$ |
| 4719.k3 |
4719j4 |
4719.k |
4719j |
$6$ |
$8$ |
\( 3 \cdot 11^{2} \cdot 13 \) |
\( 3^{2} \cdot 11^{10} \cdot 13^{4} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.17 |
2Cs |
$3432$ |
$192$ |
$1$ |
$14.99029441$ |
$1$ |
|
$2$ |
$30720$ |
$1.740044$ |
$11779205551777/3763454409$ |
$0.95747$ |
$5.25864$ |
$[1, 0, 1, -57357, -3543245]$ |
\(y^2+xy+y=x^3-57357x-3543245\) |
2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.1, 12.24.0.c.1, 24.48.0-12.c.1.1, $\ldots$ |
$[(4899983/74, 10243046817/74)]$ |
| 4719.k4 |
4719j2 |
4719.k |
4719j |
$6$ |
$8$ |
\( 3 \cdot 11^{2} \cdot 13 \) |
\( 3^{4} \cdot 11^{8} \cdot 13^{2} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.9 |
2Cs |
$3432$ |
$192$ |
$1$ |
$7.495147205$ |
$1$ |
|
$2$ |
$15360$ |
$1.393469$ |
$8732907467857/1656369$ |
$0.94339$ |
$5.22327$ |
$[1, 0, 1, -51912, -4556015]$ |
\(y^2+xy+y=x^3-51912x-4556015\) |
2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.3, 24.48.0-24.m.1.14, 44.24.0-4.b.1.3, $\ldots$ |
$[(3575/2, 202437/2)]$ |
| 4719.k5 |
4719j1 |
4719.k |
4719j |
$6$ |
$8$ |
\( 3 \cdot 11^{2} \cdot 13 \) |
\( - 3^{8} \cdot 11^{7} \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.87 |
2B |
$6864$ |
$192$ |
$1$ |
$3.747573602$ |
$1$ |
|
$3$ |
$7680$ |
$1.046896$ |
$-1532808577/938223$ |
$0.88405$ |
$4.28630$ |
$[1, 0, 1, -2907, -86759]$ |
\(y^2+xy+y=x^3-2907x-86759\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.1, 44.12.0-4.c.1.2, 48.48.0-48.g.1.5, $\ldots$ |
$[(77, 345)]$ |
| 4719.k6 |
4719j6 |
4719.k |
4719j |
$6$ |
$8$ |
\( 3 \cdot 11^{2} \cdot 13 \) |
\( - 3 \cdot 11^{8} \cdot 13^{8} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.89 |
2B |
$6864$ |
$192$ |
$1$ |
$29.98058882$ |
$1$ |
|
$0$ |
$61440$ |
$2.086617$ |
$266679605718863/296110251723$ |
$0.98475$ |
$5.62743$ |
$[1, 0, 1, 162258, -24099209]$ |
\(y^2+xy+y=x^3+162258x-24099209\) |
2.3.0.a.1, 4.6.0.c.1, 6.6.0.a.1, 8.24.0-8.n.1.7, 12.12.0.g.1, $\ldots$ |
$[(8163499195159/98050, 25000308670295585573/98050)]$ |
| 4719.l1 |
4719h1 |
4719.l |
4719h |
$1$ |
$1$ |
\( 3 \cdot 11^{2} \cdot 13 \) |
\( - 3^{5} \cdot 11^{4} \cdot 13^{4} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$3.547733139$ |
$1$ |
|
$0$ |
$7680$ |
$0.809010$ |
$-7744000000/6940323$ |
$1.07771$ |
$3.93616$ |
$[0, -1, 1, -1008, -19339]$ |
\(y^2+y=x^3-x^2-1008x-19339\) |
6.2.0.a.1 |
$[(157/2, 35/2)]$ |
| 4719.m1 |
4719m1 |
4719.m |
4719m |
$1$ |
$1$ |
\( 3 \cdot 11^{2} \cdot 13 \) |
\( - 3^{7} \cdot 11^{8} \cdot 13^{2} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$36960$ |
$1.655470$ |
$-1518309117952/369603$ |
$0.97601$ |
$5.58343$ |
$[0, 1, 1, -143304, -20932477]$ |
\(y^2+y=x^3+x^2-143304x-20932477\) |
6.2.0.a.1 |
$[]$ |
