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SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 162624co
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162624.x1 | 162624co1 | \([0, -1, 0, 3474431, -6151706207]\) | \(146234339790153527/599838494072832\) | \(-19026531525017645088768\) | \([]\) | \(12579840\) | \(2.9576\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 162624co1 has rank \(1\).
Complex multiplication
The elliptic curves in class 162624co do not have complex multiplication.Modular form 162624.2.a.co
sage: E.q_eigenform(10)