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 |
38.a1 |
38a2 |
38.a |
38a |
$3$ |
$9$ |
\( 2 \cdot 19 \) |
\( - 2^{27} \cdot 19 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
27.72.0.2 |
3B.1.2 |
$4104$ |
$1296$ |
$43$ |
$1$ |
$1$ |
|
$0$ |
$18$ |
$0.485169$ |
$-69173457625/2550136832$ |
$[1, 0, 1, -86, -2456]$ |
\(y^2+xy+y=x^3-86x-2456\) |
3.8.0-3.a.1.1, 9.24.0-9.a.1.1, 27.72.0-27.a.1.1, 152.2.0.?, 171.72.0.?, $\ldots$ |
38.a2 |
38a3 |
38.a |
38a |
$3$ |
$9$ |
\( 2 \cdot 19 \) |
\( - 2^{3} \cdot 19 \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
27.72.0.1 |
3B.1.1 |
$4104$ |
$1296$ |
$43$ |
$1$ |
$1$ |
|
$2$ |
$18$ |
$-0.613442$ |
$-413493625/152$ |
$[1, 0, 1, -16, 22]$ |
\(y^2+xy+y=x^3-16x+22\) |
3.8.0-3.a.1.2, 9.24.0-9.a.1.2, 27.72.0-27.a.1.2, 152.2.0.?, 171.72.0.?, $\ldots$ |
38.a3 |
38a1 |
38.a |
38a |
$3$ |
$9$ |
\( 2 \cdot 19 \) |
\( - 2^{9} \cdot 19^{3} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
9.72.0.3 |
3Cs.1.1 |
$4104$ |
$1296$ |
$43$ |
$1$ |
$1$ |
|
$2$ |
$6$ |
$-0.064137$ |
$94196375/3511808$ |
$[1, 0, 1, 9, 90]$ |
\(y^2+xy+y=x^3+9x+90\) |
3.24.0-3.a.1.1, 9.72.0-9.b.1.1, 152.2.0.?, 171.216.4.?, 456.48.1.?, $\ldots$ |
38.b1 |
38b2 |
38.b |
38b |
$2$ |
$5$ |
\( 2 \cdot 19 \) |
\( - 2 \cdot 19^{5} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$5$ |
5.24.0.3 |
5B.1.2 |
$760$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$10$ |
$0.017785$ |
$-37966934881/4952198$ |
$[1, 1, 1, -70, -279]$ |
\(y^2+xy+y=x^3+x^2-70x-279\) |
5.24.0-5.a.2.2, 152.2.0.?, 760.48.1.? |
38.b2 |
38b1 |
38.b |
38b |
$2$ |
$5$ |
\( 2 \cdot 19 \) |
\( - 2^{5} \cdot 19 \) |
$0$ |
$\Z/5\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$5$ |
5.24.0.1 |
5B.1.1 |
$760$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$4$ |
$2$ |
$-0.786934$ |
$-1/608$ |
$[1, 1, 1, 0, 1]$ |
\(y^2+xy+y=x^3+x^2+1\) |
5.24.0-5.a.1.2, 152.2.0.?, 760.48.1.? |