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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 8034.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8034.f1 | 8034f1 | \([1, 1, 1, -351, -2679]\) | \(-4783242408049/2715492\) | \(-2715492\) | \([]\) | \(4608\) | \(0.18112\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 8034.f1 has rank \(0\).
Complex multiplication
The elliptic curves in class 8034.f do not have complex multiplication.Modular form 8034.2.a.f
sage: E.q_eigenform(10)