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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 398502.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
398502.f1 | 398502f1 | \([1, -1, 0, -25128, -3412044]\) | \(-498677257/1145988\) | \(-4032438125180868\) | \([]\) | \(2757888\) | \(1.6829\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 398502.f1 has rank \(0\).
Complex multiplication
The elliptic curves in class 398502.f do not have complex multiplication.Modular form 398502.2.a.f
sage: E.q_eigenform(10)