Properties

Label 41650.bg
Number of curves $1$
Conductor $41650$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("bg1")
 
E.isogeny_class()
 

Elliptic curves in class 41650.bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
41650.bg1 41650w1 \([1, -1, 0, -78997, -8655739]\) \(-75659639517/1336336\) \(-962963888642000\) \([]\) \(419328\) \(1.6722\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 41650.bg1 has rank \(0\).

Complex multiplication

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

Modular form 41650.2.a.bg

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