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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 311696.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
311696.u1 | 311696u1 | \([0, -1, 0, -4931032, -4071748624]\) | \(1827347754908593/69667569664\) | \(505529751066728464384\) | \([]\) | \(9676800\) | \(2.7408\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 311696.u1 has rank \(1\).
Complex multiplication
The elliptic curves in class 311696.u do not have complex multiplication.Modular form 311696.2.a.u
sage: E.q_eigenform(10)