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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 141570f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141570.dz1 | 141570f1 | \([1, -1, 1, 1500718, 352812881]\) | \(385226073849504061/278469750000000\) | \(-270198919955250000000\) | \([]\) | \(5322240\) | \(2.6088\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 141570f1 has rank \(1\).
Complex multiplication
The elliptic curves in class 141570f do not have complex multiplication.Modular form 141570.2.a.f
sage: E.q_eigenform(10)