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 |
77.a1 |
77a1 |
77.a |
77a |
$1$ |
$1$ |
\( 7 \cdot 11 \) |
\( - 7^{2} \cdot 11 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$22$ |
$2$ |
$0$ |
$0.098027979$ |
$1$ |
|
$8$ |
$4$ |
$-0.786654$ |
$884736/539$ |
$1.02512$ |
$3.15232$ |
$[0, 0, 1, 2, 0]$ |
\(y^2+y=x^3+2x\) |
22.2.0.a.1 |
$[(2, 3)]$ |
77.b1 |
77b3 |
77.b |
77b |
$3$ |
$9$ |
\( 7 \cdot 11 \) |
\( - 7^{2} \cdot 11 \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
9.24.0.1 |
3B.1.1 |
$1386$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$2$ |
$60$ |
$-0.295000$ |
$-78843215872/539$ |
$1.00604$ |
$5.77621$ |
$[0, 1, 1, -89, 295]$ |
\(y^2+y=x^3+x^2-89x+295\) |
3.8.0-3.a.1.2, 9.24.0-9.a.1.2, 22.2.0.a.1, 63.72.0-63.e.1.2, 66.16.0-66.a.1.4, $\ldots$ |
$[ ]$ |
77.b2 |
77b1 |
77.b |
77b |
$3$ |
$9$ |
\( 7 \cdot 11 \) |
\( - 7^{6} \cdot 11^{3} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
3.24.0.1 |
3Cs.1.1 |
$1386$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$2$ |
$20$ |
$0.254306$ |
$-13278380032/156590819$ |
$1.06522$ |
$6.07112$ |
$[0, 1, 1, -49, 600]$ |
\(y^2+y=x^3+x^2-49x+600\) |
3.24.0-3.a.1.1, 22.2.0.a.1, 63.72.0-63.b.1.3, 66.48.1-66.b.1.1, 1386.144.3.? |
$[ ]$ |
77.b3 |
77b2 |
77.b |
77b |
$3$ |
$9$ |
\( 7 \cdot 11 \) |
\( - 7^{2} \cdot 11^{9} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
9.24.0.3 |
3B.1.2 |
$1386$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$0$ |
$60$ |
$0.803613$ |
$9463555063808/115539436859$ |
$1.06593$ |
$7.56918$ |
$[0, 1, 1, 441, -15815]$ |
\(y^2+y=x^3+x^2+441x-15815\) |
3.8.0-3.a.1.1, 9.24.0-9.a.1.1, 22.2.0.a.1, 63.72.0-63.e.2.2, 66.16.0-66.a.1.1, $\ldots$ |
$[ ]$ |
77.c1 |
77c2 |
77.c |
77c |
$2$ |
$2$ |
\( 7 \cdot 11 \) |
\( 7^{6} \cdot 11 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
2.3.0.1 |
2B |
$308$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$12$ |
$-0.086020$ |
$15124197817/1294139$ |
$0.97750$ |
$5.39609$ |
$[1, 1, 0, -51, 110]$ |
\(y^2+xy=x^3+x^2-51x+110\) |
2.3.0.a.1, 28.6.0.c.1, 44.6.0.a.1, 308.12.0.? |
$[ ]$ |
77.c2 |
77c1 |
77.c |
77c |
$2$ |
$2$ |
\( 7 \cdot 11 \) |
\( - 7^{3} \cdot 11^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
2.3.0.1 |
2B |
$308$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$6$ |
$-0.432593$ |
$4657463/41503$ |
$0.89262$ |
$4.14869$ |
$[1, 1, 0, 4, 11]$ |
\(y^2+xy=x^3+x^2+4x+11\) |
2.3.0.a.1, 14.6.0.b.1, 44.6.0.b.1, 308.12.0.? |
$[ ]$ |