Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 56550j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 56550.d1 | 56550j1 | \([1, 1, 0, -20325, -997875]\) | \(95093037025/11726208\) | \(114513750000000\) | \([]\) | \(319200\) | \(1.4276\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 56550j1 has rank \(1\).
Complex multiplication
The elliptic curves in class 56550j do not have complex multiplication.Modular form 56550.2.a.j
sage: E.q_eigenform(10)