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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 77658.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
77658.e1 | 77658m1 | \([1, 1, 0, -1780625, -1732344849]\) | \(-28890625/43218\) | \(-934005042615518673282\) | \([]\) | \(4045440\) | \(2.7156\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 77658.e1 has rank \(1\).
Complex multiplication
The elliptic curves in class 77658.e do not have complex multiplication.Modular form 77658.2.a.e
sage: E.q_eigenform(10)