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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 75712r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
75712.c1 | 75712r1 | \([0, 0, 0, -239980, 988157872]\) | \(-1207949625/332678528\) | \(-420944468523654053888\) | \([]\) | \(4515840\) | \(2.6366\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 75712r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 75712r do not have complex multiplication.Modular form 75712.2.a.r
sage: E.q_eigenform(10)