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SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 160080ca
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 160080.q1 | 160080ca1 | \([0, -1, 0, -1667323861, -8658837177635]\) | \(125147927114815865709295304704/64514985611316331088611125\) | \(264253381063951692138951168000\) | \([]\) | \(154103040\) | \(4.3377\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 160080ca1 has rank \(0\).
Complex multiplication
The elliptic curves in class 160080ca do not have complex multiplication.Modular form 160080.2.a.ca
sage: E.q_eigenform(10)