Properties

Label 41650x
Number of curves $1$
Conductor $41650$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 41650x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
41650.m1 41650x1 \([1, 1, 0, 1662300, 134644000]\) \(11053587253415/6565418768\) \(-301724590873606250000\) \([]\) \(1572480\) \(2.6190\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 41650x1 has rank \(1\).

Complex multiplication

The elliptic curves in class 41650x do not have complex multiplication.

Modular form 41650.2.a.x

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} - 2 q^{9} + 4 q^{11} - q^{12} - 3 q^{13} + q^{16} - q^{17} + 2 q^{18} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display