| 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 |
| 170.a1 |
170b3 |
170.a |
170b |
$4$ |
$6$ |
\( 2 \cdot 5 \cdot 17 \) |
\( 2^{24} \cdot 5^{6} \cdot 17 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2, 3$ |
8.12.0.22, 3.8.0.2 |
2B, 3B.1.2 |
$2040$ |
$384$ |
$9$ |
$1$ |
$1$ |
|
$1$ |
$480$ |
$1.117477$ |
$8010684753304969/4456448000000$ |
$1.04256$ |
$7.13026$ |
$[1, 0, 1, -4169, -20724]$ |
\(y^2+xy+y=x^3-4169x-20724\) |
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.1.2, $\ldots$ |
$[]$ |
| 170.a2 |
170b1 |
170.a |
170b |
$4$ |
$6$ |
\( 2 \cdot 5 \cdot 17 \) |
\( 2^{8} \cdot 5^{2} \cdot 17^{3} \) |
$0$ |
$\Z/6\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2, 3$ |
8.12.0.22, 3.8.0.1 |
2B, 3B.1.1 |
$2040$ |
$384$ |
$9$ |
$1$ |
$1$ |
|
$5$ |
$160$ |
$0.568171$ |
$1841373668746009/31443200$ |
$0.98941$ |
$6.84398$ |
$[1, 0, 1, -2554, 49452]$ |
\(y^2+xy+y=x^3-2554x+49452\) |
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.1.2, $\ldots$ |
$[]$ |
| 170.a3 |
170b2 |
170.a |
170b |
$4$ |
$6$ |
\( 2 \cdot 5 \cdot 17 \) |
\( - 2^{4} \cdot 5^{4} \cdot 17^{6} \) |
$0$ |
$\Z/6\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2, 3$ |
8.12.0.37, 3.8.0.1 |
2B, 3B.1.1 |
$2040$ |
$384$ |
$9$ |
$1$ |
$1$ |
|
$4$ |
$320$ |
$0.914744$ |
$-1673672305534489/241375690000$ |
$0.99210$ |
$6.86871$ |
$[1, 0, 1, -2474, 52716]$ |
\(y^2+xy+y=x^3-2474x+52716\) |
2.3.0.a.1, 3.8.0-3.a.1.2, 4.6.0.a.1, 6.24.0-6.a.1.4, 8.12.0-4.a.1.1, $\ldots$ |
$[]$ |
| 170.a4 |
170b4 |
170.a |
170b |
$4$ |
$6$ |
\( 2 \cdot 5 \cdot 17 \) |
\( - 2^{12} \cdot 5^{12} \cdot 17^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2, 3$ |
8.12.0.37, 3.8.0.2 |
2B, 3B.1.2 |
$2040$ |
$384$ |
$9$ |
$1$ |
$1$ |
|
$0$ |
$960$ |
$1.464050$ |
$479958568556831351/289000000000000$ |
$1.05690$ |
$7.92720$ |
$[1, 0, 1, 16311, -159988]$ |
\(y^2+xy+y=x^3+16311x-159988\) |
2.3.0.a.1, 3.8.0-3.a.1.1, 4.6.0.a.1, 6.24.0-6.a.1.2, 8.12.0-4.a.1.1, $\ldots$ |
$[]$ |
| 170.b1 |
170a1 |
170.b |
170a |
$2$ |
$2$ |
\( 2 \cdot 5 \cdot 17 \) |
\( 2^{4} \cdot 5^{2} \cdot 17 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.12.0.21 |
2B |
$680$ |
$48$ |
$0$ |
$0.205134543$ |
$1$ |
|
$11$ |
$16$ |
$-0.539290$ |
$47045881/6800$ |
$0.98870$ |
$3.43990$ |
$[1, 0, 1, -8, 6]$ |
\(y^2+xy+y=x^3-8x+6\) |
2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.3, 34.6.0.a.1, 68.12.0.e.1, $\ldots$ |
$[(0, 2)]$ |
| 170.b2 |
170a2 |
170.b |
170a |
$2$ |
$2$ |
\( 2 \cdot 5 \cdot 17 \) |
\( - 2^{2} \cdot 5^{4} \cdot 17^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
4.12.0.12 |
2B |
$680$ |
$48$ |
$0$ |
$0.102567271$ |
$1$ |
|
$16$ |
$32$ |
$-0.192717$ |
$214921799/722500$ |
$0.91035$ |
$4.04149$ |
$[1, 0, 1, 12, 38]$ |
\(y^2+xy+y=x^3+12x+38\) |
2.3.0.a.1, 4.12.0-4.a.1.1, 68.24.0-68.d.1.1, 680.48.0.? |
$[(-1, 5)]$ |
| 170.c1 |
170d1 |
170.c |
170d |
$2$ |
$3$ |
\( 2 \cdot 5 \cdot 17 \) |
\( - 2^{3} \cdot 5^{3} \cdot 17 \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
3.8.0.1 |
3B.1.1 |
$2040$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$12$ |
$-0.505901$ |
$-1771561/17000$ |
$0.99970$ |
$3.35960$ |
$[1, 0, 1, -3, 6]$ |
\(y^2+xy+y=x^3-3x+6\) |
3.8.0-3.a.1.2, 680.2.0.?, 2040.16.0.? |
$[]$ |
| 170.c2 |
170d2 |
170.c |
170d |
$2$ |
$3$ |
\( 2 \cdot 5 \cdot 17 \) |
\( - 2^{9} \cdot 5 \cdot 17^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
3.8.0.2 |
3B.1.2 |
$2040$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$36$ |
$0.043405$ |
$1256216039/12577280$ |
$0.94869$ |
$4.62296$ |
$[1, 0, 1, 22, -164]$ |
\(y^2+xy+y=x^3+22x-164\) |
3.8.0-3.a.1.1, 680.2.0.?, 2040.16.0.? |
$[]$ |
| 170.d1 |
170e1 |
170.d |
170e |
$1$ |
$1$ |
\( 2 \cdot 5 \cdot 17 \) |
\( - 2 \cdot 5 \cdot 17 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$680$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$20$ |
$-0.669967$ |
$-116930169/170$ |
$0.88233$ |
$3.61766$ |
$[1, -1, 0, -10, -10]$ |
\(y^2+xy=x^3-x^2-10x-10\) |
680.2.0.? |
$[]$ |
| 170.e1 |
170c2 |
170.e |
170c |
$2$ |
$3$ |
\( 2 \cdot 5 \cdot 17 \) |
\( - 2^{7} \cdot 5^{9} \cdot 17^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
3.8.0.2 |
3B.1.2 |
$2040$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$252$ |
$1.089773$ |
$-32391289681150609/1228250000000$ |
$1.00352$ |
$7.41465$ |
$[1, 0, 0, -6641, -215575]$ |
\(y^2+xy=x^3-6641x-215575\) |
3.8.0-3.a.1.1, 680.2.0.?, 2040.16.0.? |
$[]$ |
| 170.e2 |
170c1 |
170.e |
170c |
$2$ |
$3$ |
\( 2 \cdot 5 \cdot 17 \) |
\( - 2^{21} \cdot 5^{3} \cdot 17 \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
3.8.0.1 |
3B.1.1 |
$2040$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$84$ |
$0.540466$ |
$7023836099951/4456448000$ |
$0.99857$ |
$5.75964$ |
$[1, 0, 0, 399, -919]$ |
\(y^2+xy=x^3+399x-919\) |
3.8.0-3.a.1.2, 680.2.0.?, 2040.16.0.? |
$[]$ |
