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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 450840.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
450840.f1 | 450840f1 | \([0, -1, 0, 300464, -37505735]\) | \(7767586344704/6060234375\) | \(-2340469206123750000\) | \([]\) | \(6967296\) | \(2.2127\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 450840.f1 has rank \(1\).
Complex multiplication
The elliptic curves in class 450840.f do not have complex multiplication.Modular form 450840.2.a.f
sage: E.q_eigenform(10)