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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 123627.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
123627.p1 | 123627b1 | \([1, 1, 0, -124485, 30954708]\) | \(-177625/243\) | \(-291865267917204723\) | \([]\) | \(1357200\) | \(2.0438\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 123627.p1 has rank \(0\).
Complex multiplication
The elliptic curves in class 123627.p do not have complex multiplication.Modular form 123627.2.a.p
sage: E.q_eigenform(10)