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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 39289.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
39289.a1 | 39289a1 | \([0, 1, 1, -257, 1500]\) | \(1884568158208/3968189\) | \(3968189\) | \([]\) | \(9280\) | \(0.15119\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 39289.a1 has rank \(3\).
Complex multiplication
The elliptic curves in class 39289.a do not have complex multiplication.Modular form 39289.2.a.a
sage: E.q_eigenform(10)