| 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 |
| 847.a1 |
847c2 |
847.a |
847c |
$2$ |
$2$ |
\( 7 \cdot 11^{2} \) |
\( 7^{6} \cdot 11^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$308$ |
$12$ |
$0$ |
$0.591964351$ |
$1$ |
|
$6$ |
$1440$ |
$1.112928$ |
$15124197817/1294139$ |
$0.97750$ |
$5.61089$ |
$[1, 1, 1, -6234, -177484]$ |
\(y^2+xy+y=x^3+x^2-6234x-177484\) |
2.3.0.a.1, 28.6.0.c.1, 44.6.0.a.1, 308.12.0.? |
$[(138, 1201)]$ |
| 847.a2 |
847c1 |
847.a |
847c |
$2$ |
$2$ |
\( 7 \cdot 11^{2} \) |
\( - 7^{3} \cdot 11^{8} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$308$ |
$12$ |
$0$ |
$1.183928702$ |
$1$ |
|
$3$ |
$720$ |
$0.766355$ |
$4657463/41503$ |
$0.89262$ |
$4.80716$ |
$[1, 1, 1, 421, -12440]$ |
\(y^2+xy+y=x^3+x^2+421x-12440\) |
2.3.0.a.1, 14.6.0.b.1, 44.6.0.b.1, 308.12.0.? |
$[(116, 1212)]$ |
| 847.b1 |
847b1 |
847.b |
847b |
$1$ |
$1$ |
\( 7 \cdot 11^{2} \) |
\( - 7^{2} \cdot 11^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$22$ |
$2$ |
$0$ |
$0.175784754$ |
$1$ |
|
$6$ |
$480$ |
$0.412294$ |
$884736/539$ |
$1.02512$ |
$4.16518$ |
$[0, 0, 1, 242, -333]$ |
\(y^2+y=x^3+242x-333\) |
22.2.0.a.1 |
$[(55, 423)]$ |
| 847.c1 |
847a1 |
847.c |
847a |
$3$ |
$9$ |
\( 7 \cdot 11^{2} \) |
\( - 7^{2} \cdot 11^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.12.0.1 |
3B |
$1386$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$0$ |
$800$ |
$0.903948$ |
$-78843215872/539$ |
$1.00604$ |
$5.85581$ |
$[0, 1, 1, -10809, -436166]$ |
\(y^2+y=x^3+x^2-10809x-436166\) |
3.4.0.a.1, 6.8.0-3.a.1.1, 9.12.0.a.1, 18.24.0-9.a.1.1, 22.2.0.a.1, $\ldots$ |
$[]$ |
| 847.c2 |
847a2 |
847.c |
847a |
$3$ |
$9$ |
\( 7 \cdot 11^{2} \) |
\( - 7^{6} \cdot 11^{9} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.12.0.1 |
3Cs |
$1386$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$0$ |
$2400$ |
$1.453255$ |
$-13278380032/156590819$ |
$1.06522$ |
$6.04583$ |
$[0, 1, 1, -5969, -822761]$ |
\(y^2+y=x^3+x^2-5969x-822761\) |
3.12.0.a.1, 6.24.0-3.a.1.1, 22.2.0.a.1, 33.24.0-3.a.1.1, 63.36.0.b.1, $\ldots$ |
$[]$ |
| 847.c3 |
847a3 |
847.c |
847a |
$3$ |
$9$ |
\( 7 \cdot 11^{2} \) |
\( - 7^{2} \cdot 11^{15} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.12.0.1 |
3B |
$1386$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$0$ |
$7200$ |
$2.002560$ |
$9463555063808/115539436859$ |
$1.06593$ |
$7.01105$ |
$[0, 1, 1, 53321, 21262764]$ |
\(y^2+y=x^3+x^2+53321x+21262764\) |
3.4.0.a.1, 6.8.0-3.a.1.2, 9.12.0.a.1, 18.24.0-9.a.1.2, 22.2.0.a.1, $\ldots$ |
$[]$ |
