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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 169338.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
169338.p1 | 169338h1 | \([1, 1, 1, -257644, -95836915]\) | \(-13719882553/20777472\) | \(-2864350954354825728\) | \([]\) | \(3144960\) | \(2.2332\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 169338.p1 has rank \(1\).
Complex multiplication
The elliptic curves in class 169338.p do not have complex multiplication.Modular form 169338.2.a.p
sage: E.q_eigenform(10)