| 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 |
| 2541.a1 |
2541i1 |
2541.a |
2541i |
$1$ |
$1$ |
\( 3 \cdot 7 \cdot 11^{2} \) |
\( 3 \cdot 7^{7} \cdot 11^{4} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$42$ |
$2$ |
$0$ |
$0.047537998$ |
$1$ |
|
$10$ |
$4032$ |
$0.762805$ |
$25104437248/2470629$ |
$1.01230$ |
$4.27762$ |
$[0, -1, 1, -1492, 20712]$ |
\(y^2+y=x^3-x^2-1492x+20712\) |
42.2.0.a.1 |
$[(15, 38)]$ |
| 2541.b1 |
2541e1 |
2541.b |
2541e |
$1$ |
$1$ |
\( 3 \cdot 7 \cdot 11^{2} \) |
\( 3^{11} \cdot 7 \cdot 11^{2} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$42$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$2112$ |
$0.426099$ |
$313944395776/1240029$ |
$0.98990$ |
$3.98814$ |
$[0, -1, 1, -700, -6876]$ |
\(y^2+y=x^3-x^2-700x-6876\) |
42.2.0.a.1 |
$[]$ |
| 2541.c1 |
2541c1 |
2541.c |
2541c |
$1$ |
$1$ |
\( 3 \cdot 7 \cdot 11^{2} \) |
\( - 3^{2} \cdot 7^{2} \cdot 11^{2} \) |
$2$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.2.0.1 |
|
$1848$ |
$4$ |
$0$ |
$0.192856513$ |
$1$ |
|
$18$ |
$288$ |
$-0.412484$ |
$24167/441$ |
$0.87626$ |
$2.33503$ |
$[1, 1, 1, 3, 12]$ |
\(y^2+xy+y=x^3+x^2+3x+12\) |
4.2.0.a.1, 1848.4.0.? |
$[(0, 3), (7, 17)]$ |
| 2541.d1 |
2541g1 |
2541.d |
2541g |
$1$ |
$1$ |
\( 3 \cdot 7 \cdot 11^{2} \) |
\( - 3^{6} \cdot 7^{6} \cdot 11^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.2.0.1 |
|
$1848$ |
$4$ |
$0$ |
$0.126058042$ |
$1$ |
|
$8$ |
$2592$ |
$0.794211$ |
$-30515071121161/85766121$ |
$0.99491$ |
$4.57251$ |
$[1, 1, 1, -3220, 69158]$ |
\(y^2+xy+y=x^3+x^2-3220x+69158\) |
4.2.0.a.1, 1848.4.0.? |
$[(86, 618)]$ |
| 2541.e1 |
2541j2 |
2541.e |
2541j |
$2$ |
$3$ |
\( 3 \cdot 7 \cdot 11^{2} \) |
\( 3 \cdot 7^{3} \cdot 11^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$462$ |
$16$ |
$0$ |
$0.870906460$ |
$1$ |
|
$2$ |
$576$ |
$0.077485$ |
$35084566528/1029$ |
$1.04087$ |
$3.70863$ |
$[0, 1, 1, -337, 2272]$ |
\(y^2+y=x^3+x^2-337x+2272\) |
3.4.0.a.1, 33.8.0-3.a.1.1, 42.8.0.b.1, 462.16.0.? |
$[(10, 1)]$ |
| 2541.e2 |
2541j1 |
2541.e |
2541j |
$2$ |
$3$ |
\( 3 \cdot 7 \cdot 11^{2} \) |
\( 3^{3} \cdot 7 \cdot 11^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$462$ |
$16$ |
$0$ |
$0.290302153$ |
$1$ |
|
$4$ |
$192$ |
$-0.471821$ |
$360448/189$ |
$0.93152$ |
$2.24365$ |
$[0, 1, 1, -7, -5]$ |
\(y^2+y=x^3+x^2-7x-5\) |
3.4.0.a.1, 33.8.0-3.a.1.2, 42.8.0.b.1, 462.16.0.? |
$[(-1, 1)]$ |
| 2541.f1 |
2541k2 |
2541.f |
2541k |
$2$ |
$3$ |
\( 3 \cdot 7 \cdot 11^{2} \) |
\( 3 \cdot 7^{3} \cdot 11^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.2 |
3B.1.2 |
$42$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$6336$ |
$1.276434$ |
$35084566528/1029$ |
$1.04087$ |
$5.54368$ |
$[0, 1, 1, -40817, -3187585]$ |
\(y^2+y=x^3+x^2-40817x-3187585\) |
3.8.0-3.a.1.1, 42.16.0-42.b.1.3 |
$[]$ |
| 2541.f2 |
2541k1 |
2541.f |
2541k |
$2$ |
$3$ |
\( 3 \cdot 7 \cdot 11^{2} \) |
\( 3^{3} \cdot 7 \cdot 11^{8} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.1 |
3B.1.1 |
$42$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$2112$ |
$0.727127$ |
$360448/189$ |
$0.93152$ |
$4.07870$ |
$[0, 1, 1, -887, 2822]$ |
\(y^2+y=x^3+x^2-887x+2822\) |
3.8.0-3.a.1.2, 42.16.0-42.b.1.4 |
$[]$ |
| 2541.g1 |
2541f1 |
2541.g |
2541f |
$1$ |
$1$ |
\( 3 \cdot 7 \cdot 11^{2} \) |
\( - 3^{2} \cdot 7^{2} \cdot 11^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.2.0.1 |
|
$168$ |
$4$ |
$0$ |
$0.465575636$ |
$1$ |
|
$4$ |
$3168$ |
$0.786464$ |
$24167/441$ |
$0.87626$ |
$4.17008$ |
$[1, 1, 0, 361, -14406]$ |
\(y^2+xy=x^3+x^2+361x-14406\) |
4.2.0.a.1, 168.4.0.? |
$[(50, 338)]$ |
| 2541.h1 |
2541b5 |
2541.h |
2541b |
$6$ |
$8$ |
\( 3 \cdot 7 \cdot 11^{2} \) |
\( 3^{8} \cdot 7 \cdot 11^{8} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.94 |
2B |
$3696$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$19200$ |
$1.821737$ |
$10206027697760497/5557167$ |
$1.00022$ |
$6.53662$ |
$[1, 1, 0, -546801, 155401866]$ |
\(y^2+xy=x^3+x^2-546801x+155401866\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.3, 28.12.0.h.1, 44.12.0-4.c.1.1, $\ldots$ |
$[]$ |
| 2541.h2 |
2541b3 |
2541.h |
2541b |
$6$ |
$8$ |
\( 3 \cdot 7 \cdot 11^{2} \) |
\( 3^{4} \cdot 7^{2} \cdot 11^{10} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.11 |
2Cs |
$1848$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$2$ |
$9600$ |
$1.475164$ |
$2533811507137/58110129$ |
$0.95470$ |
$5.47786$ |
$[1, 1, 0, -34366, 2388775]$ |
\(y^2+xy=x^3+x^2-34366x+2388775\) |
2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.8, 24.48.0-24.i.1.6, 28.24.0.c.1, $\ldots$ |
$[]$ |
| 2541.h3 |
2541b2 |
2541.h |
2541b |
$6$ |
$8$ |
\( 3 \cdot 7 \cdot 11^{2} \) |
\( 3^{2} \cdot 7^{4} \cdot 11^{8} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.14 |
2Cs |
$1848$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$2$ |
$4800$ |
$1.128590$ |
$6570725617/2614689$ |
$0.92677$ |
$4.71834$ |
$[1, 1, 0, -4721, -71760]$ |
\(y^2+xy=x^3+x^2-4721x-71760\) |
2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.10, 12.24.0-4.b.1.2, 24.48.0-24.i.2.31, $\ldots$ |
$[]$ |
| 2541.h4 |
2541b1 |
2541.h |
2541b |
$6$ |
$8$ |
\( 3 \cdot 7 \cdot 11^{2} \) |
\( 3 \cdot 7^{2} \cdot 11^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.24.0.8 |
2B |
$3696$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$2400$ |
$0.782017$ |
$4354703137/1617$ |
$0.90109$ |
$4.66587$ |
$[1, 1, 0, -4116, -103341]$ |
\(y^2+xy=x^3+x^2-4116x-103341\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 12.12.0-4.c.1.2, 16.24.0-8.n.1.2, $\ldots$ |
$[]$ |
| 2541.h5 |
2541b6 |
2541.h |
2541b |
$6$ |
$8$ |
\( 3 \cdot 7 \cdot 11^{2} \) |
\( - 3^{2} \cdot 7 \cdot 11^{14} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.24.0.9 |
2B |
$3696$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$19200$ |
$1.821737$ |
$3288008303/13504609503$ |
$1.06765$ |
$5.76103$ |
$[1, 1, 0, 3749, 7442824]$ |
\(y^2+xy=x^3+x^2+3749x+7442824\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 14.6.0.b.1, 16.24.0-8.n.1.4, $\ldots$ |
$[]$ |
| 2541.h6 |
2541b4 |
2541.h |
2541b |
$6$ |
$8$ |
\( 3 \cdot 7 \cdot 11^{2} \) |
\( - 3 \cdot 7^{8} \cdot 11^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.93 |
2B |
$3696$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$9600$ |
$1.475164$ |
$221115865823/190238433$ |
$0.96278$ |
$5.16680$ |
$[1, 1, 0, 15244, -499011]$ |
\(y^2+xy=x^3+x^2+15244x-499011\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.5, 12.12.0-4.c.1.1, 24.48.0-24.bz.1.2, $\ldots$ |
$[]$ |
| 2541.i1 |
2541a1 |
2541.i |
2541a |
$1$ |
$1$ |
\( 3 \cdot 7 \cdot 11^{2} \) |
\( - 3^{6} \cdot 7^{6} \cdot 11^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.2.0.1 |
|
$168$ |
$4$ |
$0$ |
$1$ |
$4$ |
$2$ |
$0$ |
$28512$ |
$1.993158$ |
$-30515071121161/85766121$ |
$0.99491$ |
$6.40756$ |
$[1, 1, 0, -389622, -93997647]$ |
\(y^2+xy=x^3+x^2-389622x-93997647\) |
4.2.0.a.1, 168.4.0.? |
$[]$ |
| 2541.j1 |
2541l5 |
2541.j |
2541l |
$6$ |
$8$ |
\( 3 \cdot 7 \cdot 11^{2} \) |
\( 3 \cdot 7^{2} \cdot 11^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.24.0.13 |
2B |
$3696$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$5120$ |
$1.273153$ |
$53297461115137/147$ |
$1.05087$ |
$5.86638$ |
$[1, 0, 1, -94867, 11238599]$ |
\(y^2+xy+y=x^3-94867x+11238599\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 12.12.0.h.1, 16.24.0.e.2, $\ldots$ |
$[]$ |
| 2541.j2 |
2541l4 |
2541.j |
2541l |
$6$ |
$8$ |
\( 3 \cdot 7 \cdot 11^{2} \) |
\( 3^{2} \cdot 7^{4} \cdot 11^{6} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.18 |
2Cs |
$1848$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$2$ |
$2560$ |
$0.926579$ |
$13027640977/21609$ |
$1.08149$ |
$4.80564$ |
$[1, 0, 1, -5932, 175085]$ |
\(y^2+xy+y=x^3-5932x+175085\) |
2.6.0.a.1, 4.12.0.b.1, 8.24.0.e.1, 12.24.0.c.1, 24.48.0.j.2, $\ldots$ |
$[]$ |
| 2541.j3 |
2541l3 |
2541.j |
2541l |
$6$ |
$8$ |
\( 3 \cdot 7 \cdot 11^{2} \) |
\( 3^{8} \cdot 7 \cdot 11^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.88 |
2B |
$3696$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$2560$ |
$0.926579$ |
$6570725617/45927$ |
$1.00160$ |
$4.71834$ |
$[1, 0, 1, -4722, -124511]$ |
\(y^2+xy+y=x^3-4722x-124511\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.1, 28.12.0.h.1, 44.12.0-4.c.1.2, $\ldots$ |
$[]$ |
| 2541.j4 |
2541l6 |
2541.j |
2541l |
$6$ |
$8$ |
\( 3 \cdot 7 \cdot 11^{2} \) |
\( - 3 \cdot 7^{8} \cdot 11^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.90 |
2B |
$3696$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$5120$ |
$1.273153$ |
$-4354703137/17294403$ |
$1.04266$ |
$4.92889$ |
$[1, 0, 1, -4117, 284711]$ |
\(y^2+xy+y=x^3-4117x+284711\) |
2.3.0.a.1, 4.6.0.c.1, 6.6.0.a.1, 8.24.0.bb.2, 12.12.0.g.1, $\ldots$ |
$[]$ |
| 2541.j5 |
2541l2 |
2541.j |
2541l |
$6$ |
$8$ |
\( 3 \cdot 7 \cdot 11^{2} \) |
\( 3^{4} \cdot 7^{2} \cdot 11^{6} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.10 |
2Cs |
$1848$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$2$ |
$1280$ |
$0.580006$ |
$7189057/3969$ |
$1.14862$ |
$3.84875$ |
$[1, 0, 1, -487, 845]$ |
\(y^2+xy+y=x^3-487x+845\) |
2.6.0.a.1, 4.12.0.b.1, 8.24.0.e.2, 24.48.0.w.2, 28.24.0.c.1, $\ldots$ |
$[]$ |
| 2541.j6 |
2541l1 |
2541.j |
2541l |
$6$ |
$8$ |
\( 3 \cdot 7 \cdot 11^{2} \) |
\( - 3^{2} \cdot 7 \cdot 11^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.24.0.1 |
2B |
$3696$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$640$ |
$0.233432$ |
$103823/63$ |
$0.97868$ |
$3.30826$ |
$[1, 0, 1, 118, 119]$ |
\(y^2+xy+y=x^3+118x+119\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 14.6.0.b.1, 16.24.0.e.1, $\ldots$ |
$[]$ |
| 2541.k1 |
2541d1 |
2541.k |
2541d |
$1$ |
$1$ |
\( 3 \cdot 7 \cdot 11^{2} \) |
\( 3 \cdot 7^{7} \cdot 11^{10} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$42$ |
$2$ |
$0$ |
$1$ |
$9$ |
$3$ |
$0$ |
$44352$ |
$1.961752$ |
$25104437248/2470629$ |
$1.01230$ |
$6.11267$ |
$[0, -1, 1, -180572, -26845765]$ |
\(y^2+y=x^3-x^2-180572x-26845765\) |
42.2.0.a.1 |
$[]$ |
| 2541.l1 |
2541h1 |
2541.l |
2541h |
$1$ |
$1$ |
\( 3 \cdot 7 \cdot 11^{2} \) |
\( 3^{11} \cdot 7 \cdot 11^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$42$ |
$2$ |
$0$ |
$3.218926915$ |
$1$ |
|
$0$ |
$23232$ |
$1.625048$ |
$313944395776/1240029$ |
$0.98990$ |
$5.82319$ |
$[0, -1, 1, -84740, 9490535]$ |
\(y^2+y=x^3-x^2-84740x+9490535\) |
42.2.0.a.1 |
$[(445/2, 9555/2)]$ |
