| 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 |
| 162.a1 |
162a1 |
162.a |
162a |
$2$ |
$3$ |
\( 2 \cdot 3^{4} \) |
\( - 2^{2} \cdot 3^{6} \) |
$1$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.8.0.2, 3.8.0.1 |
3B.1.1 |
$12$ |
$128$ |
$1$ |
$0.305934883$ |
$1$ |
|
$14$ |
$12$ |
$-0.597807$ |
$-35937/4$ |
$1.00607$ |
$3.39200$ |
$[1, -1, 0, -6, 8]$ |
\(y^2+xy=x^3-x^2-6x+8\) |
3.8.0-3.a.1.2, 4.8.0.b.1, 12.128.1-12.b.2.3 |
$[(4, 4)]$ |
| 162.a2 |
162a2 |
162.a |
162a |
$2$ |
$3$ |
\( 2 \cdot 3^{4} \) |
\( - 2^{6} \cdot 3^{10} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.8.0.2, 3.8.0.2 |
3B.1.2 |
$12$ |
$128$ |
$1$ |
$0.101978294$ |
$1$ |
|
$10$ |
$36$ |
$-0.048500$ |
$109503/64$ |
$1.28549$ |
$4.44018$ |
$[1, -1, 0, 39, -19]$ |
\(y^2+xy=x^3-x^2+39x-19\) |
3.8.0-3.a.1.1, 4.8.0.b.1, 12.128.1-12.b.1.3 |
$[(10, 31)]$ |
| 162.b1 |
162c3 |
162.b |
162c |
$4$ |
$21$ |
\( 2 \cdot 3^{4} \) |
\( - 2^{7} \cdot 3^{6} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3, 7$ |
8.2.0.1, 3.8.0.1, 7.8.0.1 |
3B.1.1, 7B |
$504$ |
$768$ |
$21$ |
$1$ |
$1$ |
|
$2$ |
$42$ |
$0.269368$ |
$-189613868625/128$ |
$1.12596$ |
$6.39987$ |
$[1, -1, 0, -1077, 13877]$ |
\(y^2+xy=x^3-x^2-1077x+13877\) |
3.8.0-3.a.1.2, 7.8.0.a.1, 8.2.0.a.1, 21.128.1-21.a.4.2, 24.16.0-24.a.1.8, $\ldots$ |
$[]$ |
| 162.b2 |
162c4 |
162.b |
162c |
$4$ |
$21$ |
\( 2 \cdot 3^{4} \) |
\( - 2^{21} \cdot 3^{10} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3, 7$ |
8.2.0.1, 3.8.0.2, 7.8.0.1 |
3B.1.2, 7B |
$504$ |
$768$ |
$21$ |
$1$ |
$1$ |
|
$0$ |
$126$ |
$0.818674$ |
$-1159088625/2097152$ |
$1.11235$ |
$6.54031$ |
$[1, -1, 0, -852, 19664]$ |
\(y^2+xy=x^3-x^2-852x+19664\) |
3.8.0-3.a.1.1, 7.8.0.a.1, 8.2.0.a.1, 21.128.1-21.a.1.3, 24.16.0-24.a.1.6, $\ldots$ |
$[]$ |
| 162.b3 |
162c2 |
162.b |
162c |
$4$ |
$21$ |
\( 2 \cdot 3^{4} \) |
\( - 2^{3} \cdot 3^{10} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3, 7$ |
8.2.0.1, 3.8.0.2, 7.8.0.1 |
3B.1.2, 7B |
$504$ |
$768$ |
$21$ |
$1$ |
$1$ |
|
$0$ |
$18$ |
$-0.154281$ |
$-140625/8$ |
$1.17810$ |
$4.50778$ |
$[1, -1, 0, -42, -100]$ |
\(y^2+xy=x^3-x^2-42x-100\) |
3.8.0-3.a.1.1, 7.8.0.a.1, 8.2.0.a.1, 21.128.1-21.a.3.2, 24.16.0-24.a.1.6, $\ldots$ |
$[]$ |
| 162.b4 |
162c1 |
162.b |
162c |
$4$ |
$21$ |
\( 2 \cdot 3^{4} \) |
\( - 2 \cdot 3^{6} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3, 7$ |
8.2.0.1, 3.8.0.1, 7.8.0.1 |
3B.1.1, 7B |
$504$ |
$768$ |
$21$ |
$1$ |
$1$ |
|
$2$ |
$6$ |
$-0.703587$ |
$3375/2$ |
$1.42657$ |
$2.89249$ |
$[1, -1, 0, 3, -1]$ |
\(y^2+xy=x^3-x^2+3x-1\) |
3.8.0-3.a.1.2, 7.8.0.a.1, 8.2.0.a.1, 21.128.1-21.a.2.2, 24.16.0-24.a.1.8, $\ldots$ |
$[]$ |
| 162.c1 |
162b4 |
162.c |
162b |
$4$ |
$21$ |
\( 2 \cdot 3^{4} \) |
\( - 2^{7} \cdot 3^{12} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3, 7$ |
8.2.0.1, 3.8.0.2, 7.16.0.2 |
3B.1.2, 7B.2.3 |
$504$ |
$768$ |
$21$ |
$1$ |
$1$ |
|
$0$ |
$126$ |
$0.818674$ |
$-189613868625/128$ |
$1.12596$ |
$7.69550$ |
$[1, -1, 1, -9695, -364985]$ |
\(y^2+xy+y=x^3-x^2-9695x-364985\) |
3.8.0-3.a.1.1, 7.16.0-7.a.1.1, 8.2.0.a.1, 21.128.1-21.a.4.3, 24.16.0-24.a.1.6, $\ldots$ |
$[]$ |
| 162.c2 |
162b3 |
162.c |
162b |
$4$ |
$21$ |
\( 2 \cdot 3^{4} \) |
\( - 2^{21} \cdot 3^{4} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3, 7$ |
8.2.0.1, 3.8.0.1, 7.16.0.2 |
3B.1.1, 7B.2.3 |
$504$ |
$768$ |
$21$ |
$1$ |
$1$ |
|
$2$ |
$42$ |
$0.269368$ |
$-1159088625/2097152$ |
$1.11235$ |
$5.24467$ |
$[1, -1, 1, -95, -697]$ |
\(y^2+xy+y=x^3-x^2-95x-697\) |
3.8.0-3.a.1.2, 7.16.0-7.a.1.1, 8.2.0.a.1, 21.128.1-21.a.1.2, 24.16.0-24.a.1.8, $\ldots$ |
$[]$ |
| 162.c3 |
162b1 |
162.c |
162b |
$4$ |
$21$ |
\( 2 \cdot 3^{4} \) |
\( - 2^{3} \cdot 3^{4} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3, 7$ |
8.2.0.1, 3.8.0.1, 7.16.0.1 |
3B.1.1, 7B.2.1 |
$504$ |
$768$ |
$21$ |
$1$ |
$1$ |
|
$2$ |
$6$ |
$-0.703587$ |
$-140625/8$ |
$1.17810$ |
$3.21214$ |
$[1, -1, 1, -5, 5]$ |
\(y^2+xy+y=x^3-x^2-5x+5\) |
3.8.0-3.a.1.2, 7.16.0-7.a.1.2, 8.2.0.a.1, 21.128.1-21.a.3.3, 24.16.0-24.a.1.8, $\ldots$ |
$[]$ |
| 162.c4 |
162b2 |
162.c |
162b |
$4$ |
$21$ |
\( 2 \cdot 3^{4} \) |
\( - 2 \cdot 3^{12} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3, 7$ |
8.2.0.1, 3.8.0.2, 7.16.0.1 |
3B.1.2, 7B.2.1 |
$504$ |
$768$ |
$21$ |
$1$ |
$1$ |
|
$0$ |
$18$ |
$-0.154281$ |
$3375/2$ |
$1.42657$ |
$4.18813$ |
$[1, -1, 1, 25, 1]$ |
\(y^2+xy+y=x^3-x^2+25x+1\) |
3.8.0-3.a.1.1, 7.16.0-7.a.1.2, 8.2.0.a.1, 21.128.1-21.a.2.3, 24.16.0-24.a.1.6, $\ldots$ |
$[]$ |
| 162.d1 |
162d2 |
162.d |
162d |
$2$ |
$3$ |
\( 2 \cdot 3^{4} \) |
\( - 2^{2} \cdot 3^{12} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.16.0.2, 3.8.0.2 |
3B.1.2 |
$12$ |
$128$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$36$ |
$-0.048500$ |
$-35937/4$ |
$1.00607$ |
$4.68763$ |
$[1, -1, 1, -56, -161]$ |
\(y^2+xy+y=x^3-x^2-56x-161\) |
3.8.0-3.a.1.1, 4.16.0-4.b.1.1, 12.128.1-12.b.2.4 |
$[]$ |
| 162.d2 |
162d1 |
162.d |
162d |
$2$ |
$3$ |
\( 2 \cdot 3^{4} \) |
\( - 2^{6} \cdot 3^{4} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.16.0.2, 3.8.0.1 |
3B.1.1 |
$12$ |
$128$ |
$1$ |
$1$ |
$1$ |
|
$2$ |
$12$ |
$-0.597807$ |
$109503/64$ |
$1.28549$ |
$3.14454$ |
$[1, -1, 1, 4, -1]$ |
\(y^2+xy+y=x^3-x^2+4x-1\) |
3.8.0-3.a.1.2, 4.16.0-4.b.1.1, 12.128.1-12.b.1.4 |
$[]$ |
