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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 41038.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
41038.a1 | 41038b1 | \([1, -1, 0, -758968, 253638976]\) | \(2003092024307193/9529458688\) | \(230017966614249472\) | \([]\) | \(1492992\) | \(2.1806\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 41038.a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 41038.a do not have complex multiplication.Modular form 41038.2.a.a
sage: E.q_eigenform(10)