| 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 |
| 195.a1 |
195a7 |
195.a |
195a |
$8$ |
$16$ |
\( 3 \cdot 5 \cdot 13 \) |
\( 3 \cdot 5^{4} \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
16.48.0.44 |
2B |
$6240$ |
$768$ |
$13$ |
$1$ |
$4$ |
$2$ |
$0$ |
$384$ |
$1.189417$ |
$242970740812818720001/24375$ |
$1.04119$ |
$8.90185$ |
$[1, 0, 0, -130000, -18051943]$ |
\(y^2+xy=x^3-130000x-18051943\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 16.48.0-16.g.1.6, 24.48.0-24.by.1.11, $\ldots$ |
$[]$ |
| 195.a2 |
195a5 |
195.a |
195a |
$8$ |
$16$ |
\( 3 \cdot 5 \cdot 13 \) |
\( 3^{2} \cdot 5^{8} \cdot 13^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.48.0.35 |
2Cs |
$3120$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$2$ |
$192$ |
$0.842843$ |
$59319456301170001/594140625$ |
$1.01234$ |
$7.32443$ |
$[1, 0, 0, -8125, -282568]$ |
\(y^2+xy=x^3-8125x-282568\) |
2.6.0.a.1, 4.24.0-4.b.1.1, 8.48.0-8.i.1.2, 24.96.0-24.bb.1.1, 80.96.0.?, $\ldots$ |
$[]$ |
| 195.a3 |
195a8 |
195.a |
195a |
$8$ |
$16$ |
\( 3 \cdot 5 \cdot 13 \) |
\( - 3 \cdot 5^{16} \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
16.48.0.44 |
2B |
$6240$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$0$ |
$384$ |
$1.189417$ |
$-55150149867714721/5950927734375$ |
$1.01425$ |
$7.34303$ |
$[1, 0, 0, -7930, -296725]$ |
\(y^2+xy=x^3-7930x-296725\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 16.48.0-16.g.1.6, 24.48.0-24.bz.2.11, $\ldots$ |
$[]$ |
| 195.a4 |
195a3 |
195.a |
195a |
$8$ |
$16$ |
\( 3 \cdot 5 \cdot 13 \) |
\( 3^{4} \cdot 5^{4} \cdot 13^{4} \) |
$0$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
4.48.0.3 |
2Cs |
$3120$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$6$ |
$96$ |
$0.496270$ |
$15551989015681/1445900625$ |
$0.97384$ |
$5.76052$ |
$[1, 0, 0, -520, -4225]$ |
\(y^2+xy=x^3-520x-4225\) |
2.6.0.a.1, 4.48.0-4.b.1.1, 24.96.0-24.b.1.1, 40.96.0-40.b.2.9, 104.96.0.?, $\ldots$ |
$[]$ |
| 195.a5 |
195a2 |
195.a |
195a |
$8$ |
$16$ |
\( 3 \cdot 5 \cdot 13 \) |
\( 3^{8} \cdot 5^{2} \cdot 13^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.48.0.28 |
2Cs |
$3120$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$6$ |
$48$ |
$0.149696$ |
$168288035761/27720225$ |
$1.01793$ |
$4.90213$ |
$[1, 0, 0, -115, 392]$ |
\(y^2+xy=x^3-115x+392\) |
2.6.0.a.1, 4.24.0-4.b.1.3, 8.48.0-8.i.1.10, 40.96.0-40.bc.2.5, 48.96.0-48.d.1.6, $\ldots$ |
$[]$ |
| 195.a6 |
195a1 |
195.a |
195a |
$8$ |
$16$ |
\( 3 \cdot 5 \cdot 13 \) |
\( 3^{4} \cdot 5 \cdot 13 \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
16.48.0.28 |
2B |
$6240$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$3$ |
$24$ |
$-0.196877$ |
$147281603041/5265$ |
$0.93867$ |
$4.87685$ |
$[1, 0, 0, -110, 435]$ |
\(y^2+xy=x^3-110x+435\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 16.48.0-16.g.1.2, 40.48.0-40.cb.2.7, $\ldots$ |
$[]$ |
| 195.a7 |
195a4 |
195.a |
195a |
$8$ |
$16$ |
\( 3 \cdot 5 \cdot 13 \) |
\( - 3^{16} \cdot 5 \cdot 13 \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
16.48.0.28 |
2B |
$6240$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$2$ |
$96$ |
$0.496270$ |
$1023887723039/2798036865$ |
$1.05353$ |
$5.49383$ |
$[1, 0, 0, 210, 2277]$ |
\(y^2+xy=x^3+210x+2277\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 16.48.0-16.g.1.2, 40.48.0-40.ca.1.3, $\ldots$ |
$[]$ |
| 195.a8 |
195a6 |
195.a |
195a |
$8$ |
$16$ |
\( 3 \cdot 5 \cdot 13 \) |
\( - 3^{2} \cdot 5^{2} \cdot 13^{8} \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.48.0.60 |
2B |
$6240$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$2$ |
$192$ |
$0.842843$ |
$24487529386319/183539412225$ |
$1.01498$ |
$6.31710$ |
$[1, 0, 0, 605, -19750]$ |
\(y^2+xy=x^3+605x-19750\) |
2.3.0.a.1, 4.24.0-4.d.1.1, 8.48.0-8.q.1.2, 24.96.0-24.be.2.9, 40.96.0-40.bf.1.1, $\ldots$ |
$[]$ |
| 195.b1 |
195d1 |
195.b |
195d |
$1$ |
$1$ |
\( 3 \cdot 5 \cdot 13 \) |
\( - 3^{7} \cdot 5 \cdot 13^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$390$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$84$ |
$0.192567$ |
$-762549907456/24024195$ |
$0.97132$ |
$5.19874$ |
$[0, -1, 1, -190, 1101]$ |
\(y^2+y=x^3-x^2-190x+1101\) |
390.2.0.? |
$[]$ |
| 195.c1 |
195c1 |
195.c |
195c |
$1$ |
$1$ |
\( 3 \cdot 5 \cdot 13 \) |
\( - 3^{3} \cdot 5^{7} \cdot 13 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$390$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$84$ |
$0.124852$ |
$-32278933504/27421875$ |
$0.96372$ |
$4.76030$ |
$[0, 1, 1, -66, -349]$ |
\(y^2+y=x^3+x^2-66x-349\) |
390.2.0.? |
$[]$ |
| 195.d1 |
195b1 |
195.d |
195b |
$1$ |
$1$ |
\( 3 \cdot 5 \cdot 13 \) |
\( - 3 \cdot 5 \cdot 13 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$390$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$12$ |
$-0.880585$ |
$-4096/195$ |
$0.83662$ |
$2.41604$ |
$[0, 1, 1, 0, -1]$ |
\(y^2+y=x^3+x^2-1\) |
390.2.0.? |
$[]$ |
