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 |
Weierstrass coefficients |
Weierstrass equation |
mod-$m$ images |
MW-generators |
678.a1 |
678a1 |
678.a |
678a |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 113 \) |
\( - 2^{2} \cdot 3 \cdot 113 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$678$ |
$2$ |
$0$ |
$0.156710702$ |
$1$ |
|
$6$ |
$56$ |
$-0.560875$ |
$-217081801/1356$ |
$[1, 1, 0, -12, 12]$ |
\(y^2+xy=x^3+x^2-12x+12\) |
678.2.0.? |
$[(2, 0)]$ |
678.b1 |
678b1 |
678.b |
678b |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 113 \) |
\( - 2^{6} \cdot 3^{3} \cdot 113 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$678$ |
$2$ |
$0$ |
$0.184409578$ |
$1$ |
|
$8$ |
$72$ |
$-0.303058$ |
$30080231/195264$ |
$[1, 0, 1, 6, -20]$ |
\(y^2+xy+y=x^3+6x-20\) |
678.2.0.? |
$[(5, 9)]$ |
678.c1 |
678c1 |
678.c |
678c |
$2$ |
$2$ |
\( 2 \cdot 3 \cdot 113 \) |
\( 2^{14} \cdot 3^{4} \cdot 113 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.6.0.4 |
2B |
$904$ |
$12$ |
$0$ |
$0.249139071$ |
$1$ |
|
$13$ |
$224$ |
$0.265881$ |
$358667682625/149962752$ |
$[1, 1, 1, -148, -427]$ |
\(y^2+xy+y=x^3+x^2-148x-427\) |
2.3.0.a.1, 8.6.0.d.1, 226.6.0.?, 904.12.0.? |
$[(-7, 21)]$ |
678.c2 |
678c2 |
678.c |
678c |
$2$ |
$2$ |
\( 2 \cdot 3 \cdot 113 \) |
\( - 2^{7} \cdot 3^{8} \cdot 113^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.6.0.5 |
2B |
$904$ |
$12$ |
$0$ |
$0.498278142$ |
$1$ |
|
$8$ |
$448$ |
$0.612454$ |
$13169335133375/10723508352$ |
$[1, 1, 1, 492, -2475]$ |
\(y^2+xy+y=x^3+x^2+492x-2475\) |
2.3.0.a.1, 8.6.0.a.1, 452.6.0.?, 904.12.0.? |
$[(25, 149)]$ |
678.d1 |
678f1 |
678.d |
678f |
$2$ |
$2$ |
\( 2 \cdot 3 \cdot 113 \) |
\( 2^{2} \cdot 3^{4} \cdot 113 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.6.0.4 |
2B |
$904$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$288$ |
$-0.051439$ |
$758800078561/36612$ |
$[1, 0, 0, -190, -1024]$ |
\(y^2+xy=x^3-190x-1024\) |
2.3.0.a.1, 8.6.0.d.1, 226.6.0.?, 904.12.0.? |
$[]$ |
678.d2 |
678f2 |
678.d |
678f |
$2$ |
$2$ |
\( 2 \cdot 3 \cdot 113 \) |
\( - 2 \cdot 3^{8} \cdot 113^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.6.0.5 |
2B |
$904$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$576$ |
$0.295135$ |
$-645196518721/167554818$ |
$[1, 0, 0, -180, -1134]$ |
\(y^2+xy=x^3-180x-1134\) |
2.3.0.a.1, 8.6.0.a.1, 452.6.0.?, 904.12.0.? |
$[]$ |
678.e1 |
678d2 |
678.e |
678d |
$2$ |
$7$ |
\( 2 \cdot 3 \cdot 113 \) |
\( - 2^{2} \cdot 3 \cdot 113^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$7$ |
7.48.0.5 |
7B.1.3 |
$4746$ |
$96$ |
$2$ |
$1$ |
$1$ |
|
$0$ |
$3528$ |
$1.644447$ |
$-39934705050538129/2823126576537804$ |
$[1, 0, 0, -7121, -2567403]$ |
\(y^2+xy=x^3-7121x-2567403\) |
7.48.0-7.a.2.2, 678.2.0.?, 4746.96.2.? |
$[]$ |
678.e2 |
678d1 |
678.e |
678d |
$2$ |
$7$ |
\( 2 \cdot 3 \cdot 113 \) |
\( - 2^{14} \cdot 3^{7} \cdot 113 \) |
$0$ |
$\Z/7\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$7$ |
7.48.0.1 |
7B.1.1 |
$4746$ |
$96$ |
$2$ |
$1$ |
$1$ |
|
$6$ |
$504$ |
$0.671493$ |
$-506814405937489/4048994304$ |
$[1, 0, 0, -1661, 26097]$ |
\(y^2+xy=x^3-1661x+26097\) |
7.48.0-7.a.1.2, 678.2.0.?, 4746.96.2.? |
$[]$ |
678.f1 |
678e3 |
678.f |
678e |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 113 \) |
\( 2 \cdot 3^{16} \cdot 113 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.24.0.102 |
2B |
$904$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$640$ |
$0.686241$ |
$267301555199713/9728558946$ |
$[1, 0, 0, -1342, -18430]$ |
\(y^2+xy=x^3-1342x-18430\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.m.1.5, 452.12.0.?, 904.48.0.? |
$[]$ |
678.f2 |
678e2 |
678.f |
678e |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 113 \) |
\( 2^{2} \cdot 3^{8} \cdot 113^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.24.0.4 |
2Cs |
$904$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$320$ |
$0.339668$ |
$1054045415233/335109636$ |
$[1, 0, 0, -212, 780]$ |
\(y^2+xy=x^3-212x+780\) |
2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.b.1.2, 452.24.0.?, 904.48.0.? |
$[]$ |
678.f3 |
678e1 |
678.f |
678e |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 113 \) |
\( 2^{4} \cdot 3^{4} \cdot 113 \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.24.0.53 |
2B |
$904$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$3$ |
$160$ |
$-0.006906$ |
$783012621313/146448$ |
$[1, 0, 0, -192, 1008]$ |
\(y^2+xy=x^3-192x+1008\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.m.1.1, 226.6.0.?, 452.24.0.?, $\ldots$ |
$[]$ |
678.f4 |
678e4 |
678.f |
678e |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 113 \) |
\( - 2 \cdot 3^{4} \cdot 113^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.24.0.59 |
2B |
$904$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$640$ |
$0.686241$ |
$23647316984927/26413672482$ |
$[1, 0, 0, 598, 5478]$ |
\(y^2+xy=x^3+598x+5478\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.d.1.1, 904.48.0.? |
$[]$ |