Properties

Label 41405a
Number of curves $1$
Conductor $41405$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 41405a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
41405.n1 41405a1 \([1, 1, 0, -8453, -4588618]\) \(-2401/325\) \(-9043317838752925\) \([]\) \(282240\) \(1.7412\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 41405a1 has rank \(1\).

Complex multiplication

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

Modular form 41405.2.a.a

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