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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 1305.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1305.g1 | 1305a1 | \([0, 0, 1, 27, -61]\) | \(110592/145\) | \(-2854035\) | \([]\) | \(240\) | \(-0.075443\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1305.g1 has rank \(1\).
Complex multiplication
The elliptic curves in class 1305.g do not have complex multiplication.Modular form 1305.2.a.g
sage: E.q_eigenform(10)