| 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 |
| 1040.a1 |
1040d1 |
1040.a |
1040d |
$2$ |
$2$ |
\( 2^{4} \cdot 5 \cdot 13 \) |
\( 2^{4} \cdot 5 \cdot 13^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.22 |
2B |
$520$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$192$ |
$-0.014007$ |
$153910165504/845$ |
$0.97660$ |
$4.10714$ |
$[0, 1, 0, -281, -1910]$ |
\(y^2=x^3+x^2-281x-1910\) |
2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.2, 10.6.0.a.1, 20.12.0.e.1, $\ldots$ |
$[]$ |
| 1040.a2 |
1040d2 |
1040.a |
1040d |
$2$ |
$2$ |
\( 2^{4} \cdot 5 \cdot 13 \) |
\( - 2^{8} \cdot 5^{2} \cdot 13^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.37 |
2B |
$520$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$384$ |
$0.332567$ |
$-9115564624/714025$ |
$0.88863$ |
$4.11767$ |
$[0, 1, 0, -276, -1976]$ |
\(y^2=x^3+x^2-276x-1976\) |
2.3.0.a.1, 4.6.0.a.1, 8.12.0-4.a.1.1, 20.12.0.d.1, 40.24.0-20.d.1.6, $\ldots$ |
$[]$ |
| 1040.b1 |
1040e1 |
1040.b |
1040e |
$2$ |
$2$ |
\( 2^{4} \cdot 5 \cdot 13 \) |
\( 2^{20} \cdot 5^{5} \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.22 |
2B |
$520$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$1920$ |
$1.050098$ |
$65787589563409/10400000$ |
$0.97958$ |
$5.77737$ |
$[0, 1, 0, -13456, 596244]$ |
\(y^2=x^3+x^2-13456x+596244\) |
2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.2, 130.6.0.?, 260.24.0.?, $\ldots$ |
$[]$ |
| 1040.b2 |
1040e2 |
1040.b |
1040e |
$2$ |
$2$ |
\( 2^{4} \cdot 5 \cdot 13 \) |
\( - 2^{16} \cdot 5^{10} \cdot 13^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.37 |
2B |
$520$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$3840$ |
$1.396671$ |
$-48743122863889/26406250000$ |
$0.98824$ |
$5.82931$ |
$[0, 1, 0, -12176, 715540]$ |
\(y^2=x^3+x^2-12176x+715540\) |
2.3.0.a.1, 4.6.0.a.1, 8.12.0-4.a.1.1, 260.12.0.?, 520.48.0.? |
$[]$ |
| 1040.c1 |
1040b1 |
1040.c |
1040b |
$2$ |
$2$ |
\( 2^{4} \cdot 5 \cdot 13 \) |
\( 2^{8} \cdot 5 \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.21 |
2B |
$520$ |
$48$ |
$0$ |
$1.000344974$ |
$1$ |
|
$5$ |
$64$ |
$-0.394336$ |
$3631696/65$ |
$0.75998$ |
$2.97257$ |
$[0, 1, 0, -20, 28]$ |
\(y^2=x^3+x^2-20x+28\) |
2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.3, 130.6.0.?, 260.24.0.?, $\ldots$ |
$[(3, 2)]$ |
| 1040.c2 |
1040b2 |
1040.c |
1040b |
$2$ |
$2$ |
\( 2^{4} \cdot 5 \cdot 13 \) |
\( - 2^{10} \cdot 5^{2} \cdot 13^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.12 |
2B |
$520$ |
$48$ |
$0$ |
$0.500172487$ |
$1$ |
|
$9$ |
$128$ |
$-0.047762$ |
$-4/4225$ |
$1.09431$ |
$3.27264$ |
$[0, 1, 0, 0, 100]$ |
\(y^2=x^3+x^2+100\) |
2.3.0.a.1, 4.12.0-4.a.1.1, 260.24.0.?, 520.48.0.? |
$[(0, 10)]$ |
| 1040.d1 |
1040a3 |
1040.d |
1040a |
$4$ |
$4$ |
\( 2^{4} \cdot 5 \cdot 13 \) |
\( 2^{11} \cdot 5^{4} \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.8 |
2B |
$520$ |
$48$ |
$0$ |
$0.542615755$ |
$1$ |
|
$7$ |
$256$ |
$0.313121$ |
$9636491538/8125$ |
$0.94289$ |
$4.40673$ |
$[0, 0, 0, -563, 5138]$ |
\(y^2=x^3-563x+5138\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 40.24.0-40.y.1.14, 52.12.0-4.c.1.2, $\ldots$ |
$[(13, 4)]$ |
| 1040.d2 |
1040a2 |
1040.d |
1040a |
$4$ |
$4$ |
\( 2^{4} \cdot 5 \cdot 13 \) |
\( 2^{10} \cdot 5^{2} \cdot 13^{2} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.1 |
2Cs |
$520$ |
$48$ |
$0$ |
$1.085231510$ |
$1$ |
|
$9$ |
$128$ |
$-0.033453$ |
$8586756/4225$ |
$0.96662$ |
$3.29600$ |
$[0, 0, 0, -43, 42]$ |
\(y^2=x^3-43x+42\) |
2.6.0.a.1, 8.12.0-2.a.1.1, 20.12.0-2.a.1.1, 40.24.0-40.b.1.2, 52.12.0-2.a.1.1, $\ldots$ |
$[(-3, 12)]$ |
| 1040.d3 |
1040a1 |
1040.d |
1040a |
$4$ |
$4$ |
\( 2^{4} \cdot 5 \cdot 13 \) |
\( 2^{8} \cdot 5 \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.12 |
2B |
$520$ |
$48$ |
$0$ |
$2.170463020$ |
$1$ |
|
$3$ |
$64$ |
$-0.380026$ |
$5256144/65$ |
$0.85145$ |
$3.02579$ |
$[0, 0, 0, -23, -42]$ |
\(y^2=x^3-23x-42\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 20.12.0-4.c.1.1, 40.24.0-40.y.1.1, $\ldots$ |
$[(6, 6)]$ |
| 1040.d4 |
1040a4 |
1040.d |
1040a |
$4$ |
$4$ |
\( 2^{4} \cdot 5 \cdot 13 \) |
\( - 2^{11} \cdot 5 \cdot 13^{4} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.7 |
2B |
$520$ |
$48$ |
$0$ |
$2.170463020$ |
$1$ |
|
$3$ |
$256$ |
$0.313121$ |
$208974222/142805$ |
$0.95226$ |
$3.85525$ |
$[0, 0, 0, 157, 322]$ |
\(y^2=x^3+157x+322\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 20.12.0-4.c.1.2, 40.24.0-40.s.1.2, $\ldots$ |
$[(7, 42)]$ |
| 1040.e1 |
1040f3 |
1040.e |
1040f |
$4$ |
$4$ |
\( 2^{4} \cdot 5 \cdot 13 \) |
\( 2^{14} \cdot 5 \cdot 13 \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.48.0.39 |
2B |
$1040$ |
$192$ |
$3$ |
$1$ |
$4$ |
$2$ |
$3$ |
$768$ |
$0.888934$ |
$294889639316481/260$ |
$1.02336$ |
$5.99331$ |
$[0, 0, 0, -22187, 1272026]$ |
\(y^2=x^3-22187x+1272026\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.o.1.1, 16.48.0-16.i.1.1, 130.6.0.?, $\ldots$ |
$[]$ |
| 1040.e2 |
1040f2 |
1040.e |
1040f |
$4$ |
$4$ |
\( 2^{4} \cdot 5 \cdot 13 \) |
\( 2^{16} \cdot 5^{2} \cdot 13^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.48.0.39 |
2Cs |
$520$ |
$192$ |
$3$ |
$1$ |
$1$ |
|
$3$ |
$384$ |
$0.542360$ |
$72043225281/67600$ |
$1.01871$ |
$4.79609$ |
$[0, 0, 0, -1387, 19866]$ |
\(y^2=x^3-1387x+19866\) |
2.6.0.a.1, 4.24.0-4.a.1.1, 8.48.0-8.g.1.1, 260.48.0.?, 520.192.3.? |
$[]$ |
| 1040.e3 |
1040f4 |
1040.e |
1040f |
$4$ |
$4$ |
\( 2^{4} \cdot 5 \cdot 13 \) |
\( - 2^{14} \cdot 5^{4} \cdot 13^{4} \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.48.0.2 |
2B |
$1040$ |
$192$ |
$3$ |
$1$ |
$1$ |
|
$3$ |
$768$ |
$0.888934$ |
$-32798729601/71402500$ |
$1.04885$ |
$4.90747$ |
$[0, 0, 0, -1067, 29274]$ |
\(y^2=x^3-1067x+29274\) |
2.3.0.a.1, 4.48.0-4.c.1.1, 520.96.1.?, 1040.192.3.? |
$[]$ |
| 1040.e4 |
1040f1 |
1040.e |
1040f |
$4$ |
$4$ |
\( 2^{4} \cdot 5 \cdot 13 \) |
\( 2^{20} \cdot 5 \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.48.0.55 |
2B |
$1040$ |
$192$ |
$3$ |
$1$ |
$1$ |
|
$1$ |
$192$ |
$0.195787$ |
$33076161/16640$ |
$0.93564$ |
$3.68968$ |
$[0, 0, 0, -107, 154]$ |
\(y^2=x^3-107x+154\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.o.1.3, 16.48.0-16.i.1.3, 130.6.0.?, $\ldots$ |
$[]$ |
| 1040.f1 |
1040c1 |
1040.f |
1040c |
$2$ |
$2$ |
\( 2^{4} \cdot 5 \cdot 13 \) |
\( 2^{12} \cdot 5 \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.22 |
2B |
$520$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$128$ |
$-0.268468$ |
$117649/65$ |
$0.95681$ |
$2.87798$ |
$[0, -1, 0, -16, 0]$ |
\(y^2=x^3-x^2-16x\) |
2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.2, 130.6.0.?, 260.24.0.?, $\ldots$ |
$[]$ |
| 1040.f2 |
1040c2 |
1040.f |
1040c |
$2$ |
$2$ |
\( 2^{4} \cdot 5 \cdot 13 \) |
\( - 2^{12} \cdot 5^{2} \cdot 13^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.37 |
2B |
$520$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$256$ |
$0.078106$ |
$6967871/4225$ |
$0.89914$ |
$3.46548$ |
$[0, -1, 0, 64, -64]$ |
\(y^2=x^3-x^2+64x-64\) |
2.3.0.a.1, 4.6.0.a.1, 8.12.0-4.a.1.1, 260.12.0.?, 520.48.0.? |
$[]$ |
| 1040.g1 |
1040g3 |
1040.g |
1040g |
$4$ |
$6$ |
\( 2^{4} \cdot 5 \cdot 13 \) |
\( 2^{24} \cdot 5 \cdot 13^{3} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.12.0.21, 3.4.0.1 |
2B, 3B |
$1560$ |
$384$ |
$9$ |
$1$ |
$1$ |
|
$1$ |
$1728$ |
$0.923596$ |
$988345570681/44994560$ |
$0.95432$ |
$5.17305$ |
$[0, -1, 0, -3320, 71792]$ |
\(y^2=x^3-x^2-3320x+71792\) |
2.3.0.a.1, 3.4.0.a.1, 4.6.0.b.1, 6.12.0.a.1, 8.12.0-4.b.1.3, $\ldots$ |
$[]$ |
| 1040.g2 |
1040g1 |
1040.g |
1040g |
$4$ |
$6$ |
\( 2^{4} \cdot 5 \cdot 13 \) |
\( 2^{16} \cdot 5^{3} \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.12.0.21, 3.4.0.1 |
2B, 3B |
$1560$ |
$384$ |
$9$ |
$1$ |
$1$ |
|
$1$ |
$576$ |
$0.374290$ |
$3803721481/26000$ |
$0.90619$ |
$4.37270$ |
$[0, -1, 0, -520, -4368]$ |
\(y^2=x^3-x^2-520x-4368\) |
2.3.0.a.1, 3.4.0.a.1, 4.6.0.b.1, 6.12.0.a.1, 8.12.0-4.b.1.3, $\ldots$ |
$[]$ |
| 1040.g3 |
1040g2 |
1040.g |
1040g |
$4$ |
$6$ |
\( 2^{4} \cdot 5 \cdot 13 \) |
\( - 2^{14} \cdot 5^{6} \cdot 13^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.12.0.12, 3.4.0.1 |
2B, 3B |
$1560$ |
$384$ |
$9$ |
$1$ |
$1$ |
|
$1$ |
$1152$ |
$0.720864$ |
$-217081801/10562500$ |
$0.97746$ |
$4.60015$ |
$[0, -1, 0, -200, -10000]$ |
\(y^2=x^3-x^2-200x-10000\) |
2.3.0.a.1, 3.4.0.a.1, 4.12.0-4.a.1.1, 6.24.0-6.a.1.1, 12.96.0-12.b.1.5, $\ldots$ |
$[]$ |
| 1040.g4 |
1040g4 |
1040.g |
1040g |
$4$ |
$6$ |
\( 2^{4} \cdot 5 \cdot 13 \) |
\( - 2^{18} \cdot 5^{2} \cdot 13^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.12.0.12, 3.4.0.1 |
2B, 3B |
$1560$ |
$384$ |
$9$ |
$1$ |
$1$ |
|
$1$ |
$3456$ |
$1.270170$ |
$157376536199/7722894400$ |
$1.01877$ |
$5.54602$ |
$[0, -1, 0, 1800, 268400]$ |
\(y^2=x^3-x^2+1800x+268400\) |
2.3.0.a.1, 3.4.0.a.1, 4.12.0-4.a.1.1, 6.24.0-6.a.1.3, 12.96.0-12.b.2.1, $\ldots$ |
$[]$ |
