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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 5733.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5733.g1 | 5733e1 | \([0, 0, 1, 42, -2340]\) | \(32768/9477\) | \(-2369695419\) | \([]\) | \(1536\) | \(0.47800\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 5733.g1 has rank \(1\).
Complex multiplication
The elliptic curves in class 5733.g do not have complex multiplication.Modular form 5733.2.a.g
sage: E.q_eigenform(10)