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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 58870.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
58870.e1 | 58870b1 | \([1, -1, 0, -3669020, -2709759280]\) | \(-12983567409/31360\) | \(-13193378836294303360\) | \([]\) | \(1559040\) | \(2.5479\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 58870.e1 has rank \(0\).
Complex multiplication
The elliptic curves in class 58870.e do not have complex multiplication.Modular form 58870.2.a.e
sage: E.q_eigenform(10)