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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 56784ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
56784.bv1 | 56784ba1 | \([0, 1, 0, -320272, 77958596]\) | \(-20994006260678308/3063651608241\) | \(-530183292715754496\) | \([]\) | \(921600\) | \(2.1313\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 56784ba1 has rank \(1\).
Complex multiplication
The elliptic curves in class 56784ba do not have complex multiplication.Modular form 56784.2.a.ba
sage: E.q_eigenform(10)