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SageMath
E = EllipticCurve("cs1")
E.isogeny_class()
Elliptic curves in class 177744cs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 177744.df1 | 177744cs1 | \([0, 1, 0, -207544, -51739276]\) | \(-3261064466/1917027\) | \(-581199454580742144\) | \([]\) | \(2534400\) | \(2.1112\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 177744cs1 has rank \(1\).
Complex multiplication
The elliptic curves in class 177744cs do not have complex multiplication.Modular form 177744.2.a.cs
sage: E.q_eigenform(10)