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SageMath
E = EllipticCurve("cf1")
E.isogeny_class()
Elliptic curves in class 75712.cf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 75712.cf1 | 75712bw1 | \([0, 1, 0, 427007, 44690335]\) | \(54439939000/36924979\) | \(-5840234773283176448\) | \([]\) | \(967680\) | \(2.2896\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 75712.cf1 has rank \(0\).
Complex multiplication
The elliptic curves in class 75712.cf do not have complex multiplication.Modular form 75712.2.a.cf
sage: E.q_eigenform(10)