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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 8001.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8001.f1 | 8001e1 | \([0, 0, 1, 15, 63]\) | \(512000/2667\) | \(-1944243\) | \([]\) | \(1152\) | \(-0.11115\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 8001.f1 has rank \(1\).
Complex multiplication
The elliptic curves in class 8001.f do not have complex multiplication.Modular form 8001.2.a.f
sage: E.q_eigenform(10)