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SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 56784ca
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
56784.k1 | 56784ca1 | \([0, -1, 0, -3331384, 2342983408]\) | \(-1223745654937/907578\) | \(-3032429593820110848\) | \([]\) | \(1572480\) | \(2.4800\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 56784ca1 has rank \(1\).
Complex multiplication
The elliptic curves in class 56784ca do not have complex multiplication.Modular form 56784.2.a.ca
sage: E.q_eigenform(10)