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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 458640.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
458640.u1 | 458640u1 | \([0, 0, 0, -142128, 20632752]\) | \(-80373952512/40625\) | \(-160487308800000\) | \([]\) | \(2476800\) | \(1.6780\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 458640.u1 has rank \(1\).
Complex multiplication
The elliptic curves in class 458640.u do not have complex multiplication.Modular form 458640.2.a.u
sage: E.q_eigenform(10)