| 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 |
Weierstrass coefficients |
Weierstrass equation |
mod-$m$ images |
| 15.a1 |
15a5 |
15.a |
15a |
$8$ |
$16$ |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
16.96.0.148 |
2B |
$480$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$0$ |
$4$ |
$0.290870$ |
$1114544804970241/405$ |
$[1, 1, 1, -2160, -39540]$ |
\(y^2+xy+y=x^3+x^2-2160x-39540\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.bb.2.3, 10.6.0.a.1, 16.96.0-16.x.2.4, $\ldots$ |
| 15.a2 |
15a2 |
15.a |
15a |
$8$ |
$16$ |
\( 3 \cdot 5 \) |
\( 3^{8} \cdot 5^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.96.0.58 |
2Cs |
$240$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$2$ |
$2$ |
$-0.055704$ |
$272223782641/164025$ |
$[1, 1, 1, -135, -660]$ |
\(y^2+xy+y=x^3+x^2-135x-660\) |
2.6.0.a.1, 4.24.0-4.b.1.1, 8.96.0-8.k.1.1, 20.48.0-20.c.1.2, 40.192.1-40.cc.2.4, $\ldots$ |
| 15.a3 |
15a6 |
15.a |
15a |
$8$ |
$16$ |
\( 3 \cdot 5 \) |
\( - 3^{16} \cdot 5 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
16.96.0.153 |
2B |
$480$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$0$ |
$4$ |
$0.290870$ |
$-147281603041/215233605$ |
$[1, 1, 1, -110, -880]$ |
\(y^2+xy+y=x^3+x^2-110x-880\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.ba.2.6, 16.96.0-16.u.2.3, 20.24.0-20.h.1.1, $\ldots$ |
| 15.a4 |
15a7 |
15.a |
15a |
$8$ |
$16$ |
\( 3 \cdot 5 \) |
\( 3 \cdot 5 \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
32.96.0.5 |
2B |
$480$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$2$ |
$4$ |
$-0.402277$ |
$56667352321/15$ |
$[1, 1, 1, -80, 242]$ |
\(y^2+xy+y=x^3+x^2-80x+242\) |
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, 24.48.0-24.by.2.3, $\ldots$ |
| 15.a5 |
15a1 |
15.a |
15a |
$8$ |
$16$ |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5^{4} \) |
$0$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.96.0.3 |
2Cs |
$240$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$6$ |
$1$ |
$-0.402277$ |
$111284641/50625$ |
$[1, 1, 1, -10, -10]$ |
\(y^2+xy+y=x^3+x^2-10x-10\) |
2.6.0.a.1, 4.48.0-4.b.1.1, 8.96.0-8.b.2.9, 24.192.1-24.n.1.1, 40.192.1-40.s.1.5, $\ldots$ |
| 15.a6 |
15a3 |
15.a |
15a |
$8$ |
$16$ |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
16.96.0.7 |
2Cs |
$240$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$6$ |
$2$ |
$-0.748851$ |
$13997521/225$ |
$[1, 1, 1, -5, 2]$ |
\(y^2+xy+y=x^3+x^2-5x+2\) |
2.6.0.a.1, 4.24.0-4.b.1.3, 8.48.0-8.i.1.10, 16.96.0-16.d.2.3, 24.96.0-24.bb.2.5, $\ldots$ |
| 15.a7 |
15a8 |
15.a |
15a |
$8$ |
$16$ |
\( 3 \cdot 5 \) |
\( - 3 \cdot 5 \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
32.96.0.5 |
2B |
$480$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$3$ |
$4$ |
$-1.095425$ |
$-1/15$ |
$[1, 1, 1, 0, 0]$ |
\(y^2+xy+y=x^3+x^2\) |
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, 24.48.0-24.bz.1.3, $\ldots$ |
| 15.a8 |
15a4 |
15.a |
15a |
$8$ |
$16$ |
\( 3 \cdot 5 \) |
\( - 3^{2} \cdot 5^{8} \) |
$0$ |
$\Z/8\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.96.0.99 |
2B |
$480$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$6$ |
$2$ |
$-0.055704$ |
$4733169839/3515625$ |
$[1, 1, 1, 35, -28]$ |
\(y^2+xy+y=x^3+x^2+35x-28\) |
2.3.0.a.1, 4.24.0-4.d.1.1, 8.96.0-8.n.2.5, 24.192.1-24.cv.2.2, 80.192.1.?, $\ldots$ |
