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 |
112.a1 |
112a2 |
112.a |
112a |
$2$ |
$2$ |
\( 2^{4} \cdot 7 \) |
\( 2^{11} \cdot 7^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.6 |
2B |
$56$ |
$12$ |
$0$ |
$0.119959949$ |
$1$ |
|
$15$ |
$16$ |
$-0.234669$ |
$3543122/49$ |
$[0, 1, 0, -40, 84]$ |
\(y^2=x^3+x^2-40x+84\) |
2.3.0.a.1, 8.6.0.b.1, 28.6.0.c.1, 56.12.0.k.1 |
$[(2, 4)]$ |
112.a2 |
112a1 |
112.a |
112a |
$2$ |
$2$ |
\( 2^{4} \cdot 7 \) |
\( - 2^{10} \cdot 7 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.1 |
2B |
$56$ |
$12$ |
$0$ |
$0.239919898$ |
$1$ |
|
$11$ |
$8$ |
$-0.581243$ |
$-4/7$ |
$[0, 1, 0, 0, 4]$ |
\(y^2=x^3+x^2+4\) |
2.3.0.a.1, 8.6.0.c.1, 14.6.0.b.1, 56.12.0.n.1 |
$[(0, 2)]$ |
112.b1 |
112b3 |
112.b |
112b |
$4$ |
$4$ |
\( 2^{4} \cdot 7 \) |
\( 2^{11} \cdot 7 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.101 |
2B |
$56$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$16$ |
$-0.002033$ |
$1443468546/7$ |
$[0, 0, 0, -299, -1990]$ |
\(y^2=x^3-299x-1990\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.p.1.5, 28.12.0-4.c.1.2, 56.48.0-56.bp.1.7 |
$[]$ |
112.b2 |
112b4 |
112.b |
112b |
$4$ |
$4$ |
\( 2^{4} \cdot 7 \) |
\( 2^{11} \cdot 7^{4} \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.49 |
2B |
$56$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$3$ |
$16$ |
$-0.002033$ |
$11090466/2401$ |
$[0, 0, 0, -59, 138]$ |
\(y^2=x^3-59x+138\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.k.1.2, 56.48.0-56.v.1.3 |
$[]$ |
112.b3 |
112b2 |
112.b |
112b |
$4$ |
$4$ |
\( 2^{4} \cdot 7 \) |
\( 2^{10} \cdot 7^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.2 |
2Cs |
$56$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$3$ |
$8$ |
$-0.348607$ |
$740772/49$ |
$[0, 0, 0, -19, -30]$ |
\(y^2=x^3-19x-30\) |
2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.a.1.1, 28.24.0-28.b.1.2, 56.48.0-56.d.1.1 |
$[]$ |
112.b4 |
112b1 |
112.b |
112b |
$4$ |
$4$ |
\( 2^{4} \cdot 7 \) |
\( - 2^{8} \cdot 7 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.60 |
2B |
$56$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$4$ |
$-0.695180$ |
$432/7$ |
$[0, 0, 0, 1, -2]$ |
\(y^2=x^3+x-2\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.p.1.3, 14.6.0.b.1, 28.24.0-28.g.1.1, $\ldots$ |
$[]$ |
112.c1 |
112c6 |
112.c |
112c |
$6$ |
$18$ |
\( 2^{4} \cdot 7 \) |
\( 2^{21} \cdot 7^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.6, 9.12.0.1 |
2B, 3B |
$504$ |
$864$ |
$21$ |
$1$ |
$1$ |
|
$1$ |
$144$ |
$1.106249$ |
$2251439055699625/25088$ |
$[0, -1, 0, -43688, 3529328]$ |
\(y^2=x^3-x^2-43688x+3529328\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.b.1, 9.12.0.a.1, $\ldots$ |
$[]$ |
112.c2 |
112c5 |
112.c |
112c |
$6$ |
$18$ |
\( 2^{4} \cdot 7 \) |
\( - 2^{30} \cdot 7 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.1, 9.12.0.1 |
2B, 3B |
$504$ |
$864$ |
$21$ |
$1$ |
$1$ |
|
$1$ |
$72$ |
$0.759675$ |
$-548347731625/1835008$ |
$[0, -1, 0, -2728, 55920]$ |
\(y^2=x^3-x^2-2728x+55920\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.c.1, 9.12.0.a.1, $\ldots$ |
$[]$ |
112.c3 |
112c4 |
112.c |
112c |
$6$ |
$18$ |
\( 2^{4} \cdot 7 \) |
\( 2^{15} \cdot 7^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.6, 3.12.0.1 |
2B, 3Cs |
$504$ |
$864$ |
$21$ |
$1$ |
$1$ |
|
$1$ |
$48$ |
$0.556942$ |
$4956477625/941192$ |
$[0, -1, 0, -568, 4464]$ |
\(y^2=x^3-x^2-568x+4464\) |
2.3.0.a.1, 3.12.0.a.1, 6.36.0.a.1, 8.6.0.b.1, 12.72.0-6.a.1.1, $\ldots$ |
$[]$ |
112.c4 |
112c2 |
112.c |
112c |
$6$ |
$18$ |
\( 2^{4} \cdot 7 \) |
\( 2^{13} \cdot 7^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.6, 9.12.0.1 |
2B, 3B |
$504$ |
$864$ |
$21$ |
$1$ |
$1$ |
|
$1$ |
$16$ |
$0.007636$ |
$128787625/98$ |
$[0, -1, 0, -168, -784]$ |
\(y^2=x^3-x^2-168x-784\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.b.1, 9.12.0.a.1, $\ldots$ |
$[]$ |
112.c5 |
112c1 |
112.c |
112c |
$6$ |
$18$ |
\( 2^{4} \cdot 7 \) |
\( - 2^{14} \cdot 7 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.1, 9.12.0.1 |
2B, 3B |
$504$ |
$864$ |
$21$ |
$1$ |
$1$ |
|
$1$ |
$8$ |
$-0.338938$ |
$-15625/28$ |
$[0, -1, 0, -8, -16]$ |
\(y^2=x^3-x^2-8x-16\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.c.1, 9.12.0.a.1, $\ldots$ |
$[]$ |
112.c6 |
112c3 |
112.c |
112c |
$6$ |
$18$ |
\( 2^{4} \cdot 7 \) |
\( - 2^{18} \cdot 7^{3} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.1, 3.12.0.1 |
2B, 3Cs |
$504$ |
$864$ |
$21$ |
$1$ |
$1$ |
|
$1$ |
$24$ |
$0.210368$ |
$9938375/21952$ |
$[0, -1, 0, 72, 368]$ |
\(y^2=x^3-x^2+72x+368\) |
2.3.0.a.1, 3.12.0.a.1, 6.36.0.a.1, 8.6.0.c.1, 12.72.0-6.a.1.1, $\ldots$ |
$[]$ |