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 |
Regulator |
$Ш_{\textrm{an}}$ |
Ш primes |
Integral points |
Modular degree |
Faltings height |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
120.a1 |
120b3 |
120.a |
120b |
$4$ |
$4$ |
\( 2^{3} \cdot 3 \cdot 5 \) |
\( 2^{11} \cdot 3^{4} \cdot 5 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.7 |
2B |
$1$ |
$1$ |
|
$1$ |
$32$ |
$0.069403$ |
$546718898/405$ |
$[0, 1, 0, -216, -1296]$ |
\(y^2=x^3+x^2-216x-1296\) |
120.a2 |
120b4 |
120.a |
120b |
$4$ |
$4$ |
\( 2^{3} \cdot 3 \cdot 5 \) |
\( 2^{11} \cdot 3 \cdot 5^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.8 |
2B |
$1$ |
$1$ |
|
$1$ |
$32$ |
$0.069403$ |
$136835858/1875$ |
$[0, 1, 0, -136, 560]$ |
\(y^2=x^3+x^2-136x+560\) |
120.a3 |
120b2 |
120.a |
120b |
$4$ |
$4$ |
\( 2^{3} \cdot 3 \cdot 5 \) |
\( 2^{10} \cdot 3^{2} \cdot 5^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.1 |
2Cs |
$1$ |
$1$ |
|
$3$ |
$16$ |
$-0.277171$ |
$470596/225$ |
$[0, 1, 0, -16, -16]$ |
\(y^2=x^3+x^2-16x-16\) |
120.a4 |
120b1 |
120.a |
120b |
$4$ |
$4$ |
\( 2^{3} \cdot 3 \cdot 5 \) |
\( - 2^{8} \cdot 3 \cdot 5 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.12 |
2B |
$1$ |
$1$ |
|
$1$ |
$8$ |
$-0.623744$ |
$21296/15$ |
$[0, 1, 0, 4, 0]$ |
\(y^2=x^3+x^2+4x\) |
120.b1 |
120a5 |
120.b |
120a |
$6$ |
$8$ |
\( 2^{3} \cdot 3 \cdot 5 \) |
\( 2^{11} \cdot 3 \cdot 5^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.48.0.45 |
2B |
$1$ |
$4$ |
$2$ |
$1$ |
$64$ |
$0.479999$ |
$1770025017602/75$ |
$[0, 1, 0, -3200, -70752]$ |
\(y^2=x^3+x^2-3200x-70752\) |
120.b2 |
120a3 |
120.b |
120a |
$6$ |
$8$ |
\( 2^{3} \cdot 3 \cdot 5 \) |
\( 2^{10} \cdot 3^{2} \cdot 5^{4} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.48.0.31 |
2Cs |
$1$ |
$1$ |
|
$3$ |
$32$ |
$0.133425$ |
$868327204/5625$ |
$[0, 1, 0, -200, -1152]$ |
\(y^2=x^3+x^2-200x-1152\) |
120.b3 |
120a6 |
120.b |
120a |
$6$ |
$8$ |
\( 2^{3} \cdot 3 \cdot 5 \) |
\( - 2^{11} \cdot 3 \cdot 5^{8} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.48.0.175 |
2B |
$1$ |
$1$ |
|
$1$ |
$64$ |
$0.479999$ |
$-27995042/1171875$ |
$[0, 1, 0, -80, -2400]$ |
\(y^2=x^3+x^2-80x-2400\) |
120.b4 |
120a2 |
120.b |
120a |
$6$ |
$8$ |
\( 2^{3} \cdot 3 \cdot 5 \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.48.0.26 |
2Cs |
$1$ |
$1$ |
|
$7$ |
$16$ |
$-0.213148$ |
$3631696/2025$ |
$[0, 1, 0, -20, 0]$ |
\(y^2=x^3+x^2-20x\) |
120.b5 |
120a1 |
120.b |
120a |
$6$ |
$8$ |
\( 2^{3} \cdot 3 \cdot 5 \) |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.48.0.30 |
2B |
$1$ |
$1$ |
|
$3$ |
$8$ |
$-0.559722$ |
$24918016/45$ |
$[0, 1, 0, -15, 18]$ |
\(y^2=x^3+x^2-15x+18\) |
120.b6 |
120a4 |
120.b |
120a |
$6$ |
$8$ |
\( 2^{3} \cdot 3 \cdot 5 \) |
\( - 2^{10} \cdot 3^{8} \cdot 5 \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.48.0.160 |
2B |
$1$ |
$1$ |
|
$3$ |
$32$ |
$0.133425$ |
$54607676/32805$ |
$[0, 1, 0, 80, 80]$ |
\(y^2=x^3+x^2+80x+80\) |