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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 250470.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
250470.f1 | 250470f1 | \([1, -1, 0, -87225, -4841875]\) | \(30815752997403/13542400000\) | \(32253162163200000\) | \([]\) | \(2695680\) | \(1.8636\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 250470.f1 has rank \(1\).
Complex multiplication
The elliptic curves in class 250470.f do not have complex multiplication.Modular form 250470.2.a.f
sage: E.q_eigenform(10)