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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 56550k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
56550.f1 | 56550k1 | \([1, 1, 0, 175, -4125]\) | \(1503815/20358\) | \(-7952343750\) | \([]\) | \(38160\) | \(0.58048\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 56550k1 has rank \(0\).
Complex multiplication
The elliptic curves in class 56550k do not have complex multiplication.Modular form 56550.2.a.k
sage: E.q_eigenform(10)