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SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 355740.co
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 355740.co1 | 355740co1 | \([0, 1, 0, -6197781, -54462530025]\) | \(-205520896/9882675\) | \(-1266050385662895472147200\) | \([]\) | \(43545600\) | \(3.3048\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 355740.co1 has rank \(1\).
Complex multiplication
The elliptic curves in class 355740.co do not have complex multiplication.Modular form 355740.2.a.co
sage: E.q_eigenform(10)