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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 41405k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
41405.b1 | 41405k1 | \([0, -1, 1, -466496, -281673078]\) | \(-692224/1715\) | \(-27815437008436246715\) | \([]\) | \(1482624\) | \(2.4190\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 41405k1 has rank \(0\).
Complex multiplication
The elliptic curves in class 41405k do not have complex multiplication.Modular form 41405.2.a.k
sage: E.q_eigenform(10)