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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 80850bf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
80850.v1 | 80850bf1 | \([1, 1, 0, -5060500, 4381944400]\) | \(-568253025044575/359817216\) | \(-9074951578936320000\) | \([]\) | \(3494400\) | \(2.5790\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 80850bf1 has rank \(1\).
Complex multiplication
The elliptic curves in class 80850bf do not have complex multiplication.Modular form 80850.2.a.bf
sage: E.q_eigenform(10)