| 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 |
| 693.a1 |
693a2 |
693.a |
693a |
$2$ |
$2$ |
\( 3^{2} \cdot 7 \cdot 11 \) |
\( 3^{6} \cdot 7^{6} \cdot 11 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$308$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$288$ |
$0.463286$ |
$15124197817/1294139$ |
$0.97750$ |
$4.59121$ |
$[1, -1, 1, -464, -3432]$ |
\(y^2+xy+y=x^3-x^2-464x-3432\) |
2.3.0.a.1, 28.6.0.c.1, 44.6.0.a.1, 308.12.0.? |
$[]$ |
| 693.a2 |
693a1 |
693.a |
693a |
$2$ |
$2$ |
\( 3^{2} \cdot 7 \cdot 11 \) |
\( - 3^{6} \cdot 7^{3} \cdot 11^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$308$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$144$ |
$0.116713$ |
$4657463/41503$ |
$0.89262$ |
$3.76283$ |
$[1, -1, 1, 31, -264]$ |
\(y^2+xy+y=x^3-x^2+31x-264\) |
2.3.0.a.1, 14.6.0.b.1, 44.6.0.b.1, 308.12.0.? |
$[]$ |
| 693.b1 |
693c1 |
693.b |
693c |
$3$ |
$9$ |
\( 3^{2} \cdot 7 \cdot 11 \) |
\( - 3^{6} \cdot 7^{2} \cdot 11 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.24.0.3 |
3B.1.2 |
$1386$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$0$ |
$200$ |
$0.254306$ |
$-78843215872/539$ |
$1.00604$ |
$4.84364$ |
$[0, 0, 1, -804, -8775]$ |
\(y^2+y=x^3-804x-8775\) |
3.8.0-3.a.1.1, 9.24.0-9.a.1.1, 22.2.0.a.1, 63.72.0-63.e.1.1, 66.16.0-66.a.1.1, $\ldots$ |
$[]$ |
| 693.b2 |
693c2 |
693.b |
693c |
$3$ |
$9$ |
\( 3^{2} \cdot 7 \cdot 11 \) |
\( - 3^{6} \cdot 7^{6} \cdot 11^{3} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.24.0.1 |
3Cs.1.1 |
$1386$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$2$ |
$600$ |
$0.803613$ |
$-13278380032/156590819$ |
$1.06522$ |
$5.03949$ |
$[0, 0, 1, -444, -16650]$ |
\(y^2+y=x^3-444x-16650\) |
3.24.0-3.a.1.1, 22.2.0.a.1, 63.72.0-63.b.1.1, 66.48.1-66.b.1.1, 1386.144.3.? |
$[]$ |
| 693.b3 |
693c3 |
693.b |
693c |
$3$ |
$9$ |
\( 3^{2} \cdot 7 \cdot 11 \) |
\( - 3^{6} \cdot 7^{2} \cdot 11^{9} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.24.0.1 |
3B.1.1 |
$1386$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$2$ |
$1800$ |
$1.352919$ |
$9463555063808/115539436859$ |
$1.06593$ |
$6.03433$ |
$[0, 0, 1, 3966, 430965]$ |
\(y^2+y=x^3+3966x+430965\) |
3.8.0-3.a.1.2, 9.24.0-9.a.1.2, 22.2.0.a.1, 63.72.0-63.e.2.4, 66.16.0-66.a.1.4, $\ldots$ |
$[]$ |
| 693.c1 |
693b1 |
693.c |
693b |
$1$ |
$1$ |
\( 3^{2} \cdot 7 \cdot 11 \) |
\( - 3^{6} \cdot 7^{2} \cdot 11 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$22$ |
$2$ |
$0$ |
$0.563972113$ |
$1$ |
|
$4$ |
$56$ |
$-0.237348$ |
$884736/539$ |
$1.02512$ |
$3.10115$ |
$[0, 0, 1, 18, -7]$ |
\(y^2+y=x^3+18x-7\) |
22.2.0.a.1 |
$[(1, 3)]$ |
| 693.d1 |
693d5 |
693.d |
693d |
$6$ |
$8$ |
\( 3^{2} \cdot 7 \cdot 11 \) |
\( 3^{14} \cdot 7 \cdot 11^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.24.0.14 |
2B |
$3696$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$1280$ |
$1.172096$ |
$10206027697760497/5557167$ |
$1.00022$ |
$6.64321$ |
$[1, -1, 0, -40671, 3167194]$ |
\(y^2+xy=x^3-x^2-40671x+3167194\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 12.12.0-4.c.1.1, 16.24.0-8.n.1.6, $\ldots$ |
$[]$ |
| 693.d2 |
693d3 |
693.d |
693d |
$6$ |
$8$ |
\( 3^{2} \cdot 7 \cdot 11 \) |
\( 3^{10} \cdot 7^{2} \cdot 11^{4} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.17 |
2Cs |
$1848$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$2$ |
$640$ |
$0.825522$ |
$2533811507137/58110129$ |
$0.95470$ |
$5.37414$ |
$[1, -1, 0, -2556, 49387]$ |
\(y^2+xy=x^3-x^2-2556x+49387\) |
2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.1, 12.24.0-4.b.1.1, 24.48.0-24.i.1.2, $\ldots$ |
$[]$ |
| 693.d3 |
693d2 |
693.d |
693d |
$6$ |
$8$ |
\( 3^{2} \cdot 7 \cdot 11 \) |
\( 3^{8} \cdot 7^{4} \cdot 11^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.9 |
2Cs |
$1848$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$2$ |
$320$ |
$0.478949$ |
$6570725617/2614689$ |
$0.92677$ |
$4.46376$ |
$[1, -1, 0, -351, -1328]$ |
\(y^2+xy=x^3-x^2-351x-1328\) |
2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.3, 12.24.0-4.b.1.3, 24.48.0-24.i.2.2, $\ldots$ |
$[]$ |
| 693.d4 |
693d1 |
693.d |
693d |
$6$ |
$8$ |
\( 3^{2} \cdot 7 \cdot 11 \) |
\( 3^{7} \cdot 7^{2} \cdot 11 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.24.0.3 |
2B |
$3696$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$160$ |
$0.132375$ |
$4354703137/1617$ |
$0.90109$ |
$4.40087$ |
$[1, -1, 0, -306, -1985]$ |
\(y^2+xy=x^3-x^2-306x-1985\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 12.12.0-4.c.1.2, 16.24.0-8.n.1.5, $\ldots$ |
$[]$ |
| 693.d5 |
693d6 |
693.d |
693d |
$6$ |
$8$ |
\( 3^{2} \cdot 7 \cdot 11 \) |
\( - 3^{8} \cdot 7 \cdot 11^{8} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.89 |
2B |
$3696$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$1280$ |
$1.172096$ |
$3288008303/13504609503$ |
$1.06765$ |
$5.71356$ |
$[1, -1, 0, 279, 150880]$ |
\(y^2+xy=x^3-x^2+279x+150880\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.7, 12.12.0-4.c.1.1, 14.6.0.b.1, $\ldots$ |
$[]$ |
| 693.d6 |
693d4 |
693.d |
693d |
$6$ |
$8$ |
\( 3^{2} \cdot 7 \cdot 11 \) |
\( - 3^{7} \cdot 7^{8} \cdot 11 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.87 |
2B |
$3696$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$640$ |
$0.825522$ |
$221115865823/190238433$ |
$0.96278$ |
$5.00130$ |
$[1, -1, 0, 1134, -10535]$ |
\(y^2+xy=x^3-x^2+1134x-10535\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.1, 12.12.0-4.c.1.2, 24.48.0-24.bz.1.7, $\ldots$ |
$[]$ |
