Properties

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

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 41405e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
41405.k1 41405e1 \([1, 1, 0, -18008, 948823]\) \(-32485001809/1071875\) \(-21311748696875\) \([]\) \(103680\) \(1.3323\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 41405e1 has rank \(0\).

Complex multiplication

The elliptic curves in class 41405e do not have complex multiplication.

Modular form 41405.2.a.e

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} - q^{4} - q^{5} - q^{6} - 3 q^{8} - 2 q^{9} - q^{10} + 4 q^{11} + q^{12} + q^{15} - q^{16} + 7 q^{17} - 2 q^{18} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display