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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 271950.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
271950.r1 | 271950r1 | \([1, 1, 0, -31525, -1989875]\) | \(4525790192161/414305280\) | \(317202480000000\) | \([]\) | \(1612800\) | \(1.5216\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 271950.r1 has rank \(0\).
Complex multiplication
The elliptic curves in class 271950.r do not have complex multiplication.Modular form 271950.2.a.r
sage: E.q_eigenform(10)