Properties

Label 41405k
Number of curves $1$
Conductor $41405$
CM no
Rank $0$

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Show commands: 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)
 
\(q - 2 q^{2} - q^{3} + 2 q^{4} - q^{5} + 2 q^{6} - 2 q^{9} + 2 q^{10} - 5 q^{11} - 2 q^{12} + q^{15} - 4 q^{16} - 2 q^{17} + 4 q^{18} + 6 q^{19} + O(q^{20})\) Copy content Toggle raw display