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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 12675g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12675.k1 | 12675g1 | \([1, 1, 1, -371888, 130109156]\) | \(-4225/3\) | \(-4038823003388671875\) | \([]\) | \(196560\) | \(2.2701\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 12675g1 has rank \(1\).
Complex multiplication
The elliptic curves in class 12675g do not have complex multiplication.Modular form 12675.2.a.g
sage: E.q_eigenform(10)