Properties

Label 41405.s
Number of curves $1$
Conductor $41405$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 41405.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
41405.s1 41405q1 \([0, 0, 1, -637, 311015]\) \(-1437696/2100875\) \(-41771027445875\) \([]\) \(120960\) \(1.2926\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 41405.s1 has rank \(1\).

Complex multiplication

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

Modular form 41405.2.a.s

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