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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 400710.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
400710.f1 | 400710f1 | \([1, 1, 0, -6543, 202947]\) | \(-85832345136529/949743750\) | \(-342857493750\) | \([]\) | \(691200\) | \(1.0284\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 400710.f1 has rank \(1\).
Complex multiplication
The elliptic curves in class 400710.f do not have complex multiplication.Modular form 400710.2.a.f
sage: E.q_eigenform(10)