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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 41650.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
41650.q1 | 41650q1 | \([1, -1, 0, 498958, 7031366]\) | \(3112538751/1806250\) | \(-7972201851660156250\) | \([]\) | \(725760\) | \(2.3163\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 41650.q1 has rank \(1\).
Complex multiplication
The elliptic curves in class 41650.q do not have complex multiplication.Modular form 41650.2.a.q
sage: E.q_eigenform(10)