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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 27225z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
27225.q1 | 27225z1 | \([1, -1, 1, -5105, 759322]\) | \(-675/11\) | \(-239728741745625\) | \([]\) | \(69120\) | \(1.4405\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 27225z1 has rank \(1\).
Complex multiplication
The elliptic curves in class 27225z do not have complex multiplication.Modular form 27225.2.a.z
sage: E.q_eigenform(10)