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SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 159936.ca
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 159936.ca1 | 159936dk1 | \([0, -1, 0, -1731, 28449]\) | \(-76225024/459\) | \(-3456057024\) | \([]\) | \(69120\) | \(0.66991\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 159936.ca1 has rank \(1\).
Complex multiplication
The elliptic curves in class 159936.ca do not have complex multiplication.Modular form 159936.2.a.ca
sage: E.q_eigenform(10)