| 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 |
| 5577.a1 |
5577d3 |
5577.a |
5577d |
$4$ |
$4$ |
\( 3 \cdot 11 \cdot 13^{2} \) |
\( 3^{3} \cdot 11^{4} \cdot 13^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$3432$ |
$48$ |
$0$ |
$1.184501454$ |
$1$ |
|
$6$ |
$13824$ |
$1.269842$ |
$347873904937/395307$ |
$1.00913$ |
$4.86469$ |
$[1, 1, 1, -24762, 1487988]$ |
\(y^2+xy+y=x^3+x^2-24762x+1487988\) |
2.3.0.a.1, 4.6.0.c.1, 12.12.0.h.1, 52.12.0-4.c.1.2, 88.12.0.?, $\ldots$ |
$[(96, 36)]$ |
| 5577.a2 |
5577d2 |
5577.a |
5577d |
$4$ |
$4$ |
\( 3 \cdot 11 \cdot 13^{2} \) |
\( 3^{6} \cdot 11^{2} \cdot 13^{6} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.6.0.1 |
2Cs |
$1716$ |
$48$ |
$0$ |
$2.369002909$ |
$1$ |
|
$6$ |
$6912$ |
$0.923269$ |
$169112377/88209$ |
$1.00669$ |
$3.98031$ |
$[1, 1, 1, -1947, 9576]$ |
\(y^2+xy+y=x^3+x^2-1947x+9576\) |
2.6.0.a.1, 12.12.0.a.1, 44.12.0.b.1, 52.12.0-2.a.1.1, 132.24.0.?, $\ldots$ |
$[(-20, 212)]$ |
| 5577.a3 |
5577d1 |
5577.a |
5577d |
$4$ |
$4$ |
\( 3 \cdot 11 \cdot 13^{2} \) |
\( 3^{3} \cdot 11 \cdot 13^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$3432$ |
$48$ |
$0$ |
$4.738005818$ |
$1$ |
|
$1$ |
$3456$ |
$0.576695$ |
$30664297/297$ |
$1.09706$ |
$3.78238$ |
$[1, 1, 1, -1102, -14422]$ |
\(y^2+xy+y=x^3+x^2-1102x-14422\) |
2.3.0.a.1, 4.6.0.c.1, 24.12.0.ba.1, 66.6.0.a.1, 88.12.0.?, $\ldots$ |
$[(-164/3, 335/3)]$ |
| 5577.a4 |
5577d4 |
5577.a |
5577d |
$4$ |
$4$ |
\( 3 \cdot 11 \cdot 13^{2} \) |
\( - 3^{12} \cdot 11 \cdot 13^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$3432$ |
$48$ |
$0$ |
$4.738005818$ |
$1$ |
|
$0$ |
$13824$ |
$1.269842$ |
$9090072503/5845851$ |
$1.03763$ |
$4.44219$ |
$[1, 1, 1, 7348, 83936]$ |
\(y^2+xy+y=x^3+x^2+7348x+83936\) |
2.3.0.a.1, 4.6.0.c.1, 22.6.0.a.1, 24.12.0.ba.1, 44.12.0.g.1, $\ldots$ |
$[(955/3, 37424/3)]$ |
| 5577.b1 |
5577f1 |
5577.b |
5577f |
$1$ |
$1$ |
\( 3 \cdot 11 \cdot 13^{2} \) |
\( - 3^{3} \cdot 11^{2} \cdot 13^{10} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$16848$ |
$1.501127$ |
$5537792/3267$ |
$1.08782$ |
$4.77332$ |
$[0, -1, 1, 19041, -147301]$ |
\(y^2+y=x^3-x^2+19041x-147301\) |
6.2.0.a.1 |
$[]$ |
| 5577.c1 |
5577b1 |
5577.c |
5577b |
$1$ |
$1$ |
\( 3 \cdot 11 \cdot 13^{2} \) |
\( - 3^{7} \cdot 11^{2} \cdot 13^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$0.638888859$ |
$1$ |
|
$4$ |
$2352$ |
$0.505792$ |
$-2830523957248/264627$ |
$1.07225$ |
$3.91838$ |
$[0, -1, 1, -1629, 25859]$ |
\(y^2+y=x^3-x^2-1629x+25859\) |
6.2.0.a.1 |
$[(23, 5)]$ |
| 5577.d1 |
5577e1 |
5577.d |
5577e |
$1$ |
$1$ |
\( 3 \cdot 11 \cdot 13^{2} \) |
\( - 3^{7} \cdot 11^{2} \cdot 13^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$30576$ |
$1.788267$ |
$-2830523957248/264627$ |
$1.07225$ |
$5.70240$ |
$[0, -1, 1, -275357, 55711424]$ |
\(y^2+y=x^3-x^2-275357x+55711424\) |
6.2.0.a.1 |
$[]$ |
| 5577.e1 |
5577a1 |
5577.e |
5577a |
$1$ |
$1$ |
\( 3 \cdot 11 \cdot 13^{2} \) |
\( - 3^{3} \cdot 11^{2} \cdot 13^{4} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$1.427973017$ |
$1$ |
|
$2$ |
$1296$ |
$0.218653$ |
$5537792/3267$ |
$1.08782$ |
$2.98930$ |
$[0, -1, 1, 113, -102]$ |
\(y^2+y=x^3-x^2+113x-102\) |
6.2.0.a.1 |
$[(6, 27)]$ |
| 5577.f1 |
5577c2 |
5577.f |
5577c |
$2$ |
$2$ |
\( 3 \cdot 11 \cdot 13^{2} \) |
\( 3 \cdot 11^{2} \cdot 13^{8} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$1716$ |
$12$ |
$0$ |
$2.106537549$ |
$1$ |
|
$2$ |
$5376$ |
$0.911110$ |
$244140625/61347$ |
$1.08894$ |
$4.02287$ |
$[1, 1, 0, -2200, 28969]$ |
\(y^2+xy=x^3+x^2-2200x+28969\) |
2.3.0.a.1, 12.6.0.a.1, 572.6.0.?, 1716.12.0.? |
$[(96, 797)]$ |
| 5577.f2 |
5577c1 |
5577.f |
5577c |
$2$ |
$2$ |
\( 3 \cdot 11 \cdot 13^{2} \) |
\( - 3^{2} \cdot 11 \cdot 13^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$1716$ |
$12$ |
$0$ |
$4.213075099$ |
$1$ |
|
$1$ |
$2688$ |
$0.564536$ |
$857375/1287$ |
$0.79548$ |
$3.42176$ |
$[1, 1, 0, 335, 3112]$ |
\(y^2+xy=x^3+x^2+335x+3112\) |
2.3.0.a.1, 12.6.0.b.1, 286.6.0.?, 1716.12.0.? |
$[(43/2, 677/2)]$ |
| 5577.g1 |
5577g4 |
5577.g |
5577g |
$6$ |
$8$ |
\( 3 \cdot 11 \cdot 13^{2} \) |
\( 3^{2} \cdot 11 \cdot 13^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.24.0.3 |
2B |
$6864$ |
$192$ |
$1$ |
$8.564040118$ |
$1$ |
|
$0$ |
$43008$ |
$1.823570$ |
$35765103905346817/1287$ |
$0.98956$ |
$6.20252$ |
$[1, 0, 1, -1160020, 480793679]$ |
\(y^2+xy+y=x^3-1160020x+480793679\) |
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.1.4, $\ldots$ |
$[(145417/8, 49522351/8)]$ |
| 5577.g2 |
5577g5 |
5577.g |
5577g |
$6$ |
$8$ |
\( 3 \cdot 11 \cdot 13^{2} \) |
\( 3 \cdot 11^{8} \cdot 13^{8} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.89 |
2B |
$6864$ |
$192$ |
$1$ |
$4.282020059$ |
$1$ |
|
$0$ |
$86016$ |
$2.170143$ |
$3013001140430737/108679952667$ |
$0.97853$ |
$5.91572$ |
$[1, 0, 1, -508525, -135200167]$ |
\(y^2+xy+y=x^3-508525x-135200167\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.7, 12.12.0.h.1, 24.48.0-24.bl.1.2, $\ldots$ |
$[(-3293/3, 42275/3)]$ |
| 5577.g3 |
5577g3 |
5577.g |
5577g |
$6$ |
$8$ |
\( 3 \cdot 11 \cdot 13^{2} \) |
\( 3^{2} \cdot 11^{4} \cdot 13^{10} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.17 |
2Cs |
$3432$ |
$192$ |
$1$ |
$8.564040118$ |
$1$ |
|
$2$ |
$43008$ |
$1.823570$ |
$11779205551777/3763454409$ |
$0.95747$ |
$5.27300$ |
$[1, 0, 1, -80110, 5834051]$ |
\(y^2+xy+y=x^3-80110x+5834051\) |
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.1.10, $\ldots$ |
$[(8743/2, 802153/2)]$ |
| 5577.g4 |
5577g2 |
5577.g |
5577g |
$6$ |
$8$ |
\( 3 \cdot 11 \cdot 13^{2} \) |
\( 3^{4} \cdot 11^{2} \cdot 13^{8} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.9 |
2Cs |
$3432$ |
$192$ |
$1$ |
$4.282020059$ |
$1$ |
|
$4$ |
$21504$ |
$1.476997$ |
$8732907467857/1656369$ |
$0.94339$ |
$5.23831$ |
$[1, 0, 1, -72505, 7507151]$ |
\(y^2+xy+y=x^3-72505x+7507151\) |
2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.3, 24.48.0-24.m.1.7, 44.24.0-4.b.1.2, $\ldots$ |
$[(2185, 100307)]$ |
| 5577.g5 |
5577g1 |
5577.g |
5577g |
$6$ |
$8$ |
\( 3 \cdot 11 \cdot 13^{2} \) |
\( - 3^{8} \cdot 11 \cdot 13^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.87 |
2B |
$6864$ |
$192$ |
$1$ |
$2.141010029$ |
$1$ |
|
$3$ |
$10752$ |
$1.130423$ |
$-1532808577/938223$ |
$0.88405$ |
$4.31949$ |
$[1, 0, 1, -4060, 142469]$ |
\(y^2+xy+y=x^3-4060x+142469\) |
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.1.28, $\ldots$ |
$[(31, 200)]$ |
| 5577.g6 |
5577g6 |
5577.g |
5577g |
$6$ |
$8$ |
\( 3 \cdot 11 \cdot 13^{2} \) |
\( - 3 \cdot 11^{2} \cdot 13^{14} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.24.0.14 |
2B |
$6864$ |
$192$ |
$1$ |
$17.12808023$ |
$1$ |
|
$0$ |
$86016$ |
$2.170143$ |
$266679605718863/296110251723$ |
$0.98475$ |
$5.63465$ |
$[1, 0, 1, 226625, 39820289]$ |
\(y^2+xy+y=x^3+226625x+39820289\) |
2.3.0.a.1, 4.6.0.c.1, 6.6.0.a.1, 8.12.0.n.1, 12.12.0.g.1, $\ldots$ |
$[(24231903/106, 121108111333/106)]$ |
