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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 50008a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
50008.f1 | 50008a1 | \([0, 1, 0, 209, 5158]\) | \(62800480256/735423899\) | \(-11766782384\) | \([]\) | \(21504\) | \(0.61330\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 50008a1 has rank \(0\).
Complex multiplication
The elliptic curves in class 50008a do not have complex multiplication.Modular form 50008.2.a.a
sage: E.q_eigenform(10)