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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 75712.bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
75712.bc1 | 75712cb1 | \([0, -1, 0, -65121, 6420673]\) | \(-193100552/91\) | \(-14393003835392\) | \([]\) | \(365568\) | \(1.4805\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 75712.bc1 has rank \(0\).
Complex multiplication
The elliptic curves in class 75712.bc do not have complex multiplication.Modular form 75712.2.a.bc
sage: E.q_eigenform(10)