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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 5056.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5056.p1 | 5056l1 | \([0, 1, 0, -65, -193]\) | \(470596/79\) | \(5177344\) | \([]\) | \(1024\) | \(0.0093345\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 5056.p1 has rank \(0\).
Complex multiplication
The elliptic curves in class 5056.p do not have complex multiplication.Modular form 5056.2.a.p
sage: E.q_eigenform(10)