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SageMath
E = EllipticCurve("cz1")
E.isogeny_class()
Elliptic curves in class 75712cz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 75712.k1 | 75712cz1 | \([0, 1, 0, 313439, -142285857]\) | \(15925559/50176\) | \(-10729581355177345024\) | \([]\) | \(1198080\) | \(2.3349\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 75712cz1 has rank \(1\).
Complex multiplication
The elliptic curves in class 75712cz do not have complex multiplication.Modular form 75712.2.a.cz
sage: E.q_eigenform(10)