| 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 |
| 130.a1 |
130a3 |
130.a |
130a |
$4$ |
$6$ |
\( 2 \cdot 5 \cdot 13 \) |
\( 2^{12} \cdot 5 \cdot 13^{3} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2, 3$ |
8.12.0.21, 3.8.0.2 |
2B, 3B.1.2 |
$1560$ |
$384$ |
$9$ |
$0.390154717$ |
$1$ |
|
$7$ |
$72$ |
$0.230449$ |
$988345570681/44994560$ |
$0.95432$ |
$5.67419$ |
$[1, 0, 1, -208, -1122]$ |
\(y^2+xy+y=x^3-208x-1122\) |
2.3.0.a.1, 3.8.0-3.a.1.1, 4.6.0.b.1, 6.24.0-6.a.1.2, 8.12.0-4.b.1.3, $\ldots$ |
$[(-8, 10)]$ |
| 130.a2 |
130a1 |
130.a |
130a |
$4$ |
$6$ |
\( 2 \cdot 5 \cdot 13 \) |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
$1$ |
$\Z/6\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2, 3$ |
8.12.0.21, 3.8.0.1 |
2B, 3B.1.1 |
$1560$ |
$384$ |
$9$ |
$1.170464153$ |
$1$ |
|
$13$ |
$24$ |
$-0.318857$ |
$3803721481/26000$ |
$0.90619$ |
$4.53191$ |
$[1, 0, 1, -33, 68]$ |
\(y^2+xy+y=x^3-33x+68\) |
2.3.0.a.1, 3.8.0-3.a.1.2, 4.6.0.b.1, 6.24.0-6.a.1.4, 8.12.0-4.b.1.3, $\ldots$ |
$[(2, 2)]$ |
| 130.a3 |
130a2 |
130.a |
130a |
$4$ |
$6$ |
\( 2 \cdot 5 \cdot 13 \) |
\( - 2^{2} \cdot 5^{6} \cdot 13^{2} \) |
$1$ |
$\Z/6\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2, 3$ |
4.12.0.12, 3.8.0.1 |
2B, 3B.1.1 |
$1560$ |
$384$ |
$9$ |
$0.585232076$ |
$1$ |
|
$20$ |
$48$ |
$0.027717$ |
$-217081801/10562500$ |
$0.97746$ |
$4.85654$ |
$[1, 0, 1, -13, 156]$ |
\(y^2+xy+y=x^3-13x+156\) |
2.3.0.a.1, 3.8.0-3.a.1.2, 4.12.0-4.a.1.1, 6.24.0-6.a.1.4, 12.96.0-12.b.1.3, $\ldots$ |
$[(5, 12)]$ |
| 130.a4 |
130a4 |
130.a |
130a |
$4$ |
$6$ |
\( 2 \cdot 5 \cdot 13 \) |
\( - 2^{6} \cdot 5^{2} \cdot 13^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2, 3$ |
4.12.0.12, 3.8.0.2 |
2B, 3B.1.2 |
$1560$ |
$384$ |
$9$ |
$0.195077358$ |
$1$ |
|
$14$ |
$144$ |
$0.577023$ |
$157376536199/7722894400$ |
$1.01877$ |
$6.20649$ |
$[1, 0, 1, 112, -4194]$ |
\(y^2+xy+y=x^3+112x-4194\) |
2.3.0.a.1, 3.8.0-3.a.1.1, 4.12.0-4.a.1.1, 6.24.0-6.a.1.2, 12.96.0-12.b.2.7, $\ldots$ |
$[(17, 43)]$ |
| 130.b1 |
130b3 |
130.b |
130b |
$4$ |
$4$ |
\( 2 \cdot 5 \cdot 13 \) |
\( 2^{2} \cdot 5 \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
16.48.0.55 |
2B |
$1040$ |
$192$ |
$3$ |
$1$ |
$4$ |
$2$ |
$0$ |
$32$ |
$0.195787$ |
$294889639316481/260$ |
$1.02336$ |
$6.84487$ |
$[1, -1, 1, -1387, -19529]$ |
\(y^2+xy+y=x^3-x^2-1387x-19529\) |
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.?, $\ldots$ |
$[]$ |
| 130.b2 |
130b2 |
130.b |
130b |
$4$ |
$4$ |
\( 2 \cdot 5 \cdot 13 \) |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.48.0.39 |
2Cs |
$520$ |
$192$ |
$3$ |
$1$ |
$1$ |
|
$2$ |
$16$ |
$-0.150787$ |
$72043225281/67600$ |
$1.01871$ |
$5.13618$ |
$[1, -1, 1, -87, -289]$ |
\(y^2+xy+y=x^3-x^2-87x-289\) |
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.? |
$[]$ |
| 130.b3 |
130b4 |
130.b |
130b |
$4$ |
$4$ |
\( 2 \cdot 5 \cdot 13 \) |
\( - 2^{2} \cdot 5^{4} \cdot 13^{4} \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
4.48.0.2 |
2B |
$1040$ |
$192$ |
$3$ |
$1$ |
$1$ |
|
$2$ |
$32$ |
$0.195787$ |
$-32798729601/71402500$ |
$1.04885$ |
$5.29514$ |
$[1, -1, 1, -67, -441]$ |
\(y^2+xy+y=x^3-x^2-67x-441\) |
2.3.0.a.1, 4.48.0-4.c.1.1, 520.96.1.?, 1040.192.3.? |
$[]$ |
| 130.b4 |
130b1 |
130.b |
130b |
$4$ |
$4$ |
\( 2 \cdot 5 \cdot 13 \) |
\( 2^{8} \cdot 5 \cdot 13 \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
16.48.0.39 |
2B |
$1040$ |
$192$ |
$3$ |
$1$ |
$1$ |
|
$3$ |
$8$ |
$-0.497360$ |
$33076161/16640$ |
$0.93564$ |
$3.55710$ |
$[1, -1, 1, -7, -1]$ |
\(y^2+xy+y=x^3-x^2-7x-1\) |
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.?, $\ldots$ |
$[]$ |
| 130.c1 |
130c1 |
130.c |
130c |
$2$ |
$2$ |
\( 2 \cdot 5 \cdot 13 \) |
\( 2^{8} \cdot 5^{5} \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.12.0.22 |
2B |
$520$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$80$ |
$0.356951$ |
$65787589563409/10400000$ |
$0.97958$ |
$6.53667$ |
$[1, 1, 1, -841, -9737]$ |
\(y^2+xy+y=x^3+x^2-841x-9737\) |
2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.2, 130.6.0.?, 260.24.0.?, $\ldots$ |
$[]$ |
| 130.c2 |
130c2 |
130.c |
130c |
$2$ |
$2$ |
\( 2 \cdot 5 \cdot 13 \) |
\( - 2^{4} \cdot 5^{10} \cdot 13^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.12.0.37 |
2B |
$520$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$160$ |
$0.703525$ |
$-48743122863889/26406250000$ |
$0.98824$ |
$6.61080$ |
$[1, 1, 1, -761, -11561]$ |
\(y^2+xy+y=x^3+x^2-761x-11561\) |
2.3.0.a.1, 4.6.0.a.1, 8.12.0-4.a.1.1, 260.12.0.?, 520.48.0.? |
$[]$ |
