Properties

Label 41650.e
Number of curves $1$
Conductor $41650$
CM no
Rank $2$

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

Elliptic curves in class 41650.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
41650.e1 41650f1 \([1, 0, 1, -833026, 394008948]\) \(-709731835729/334084000\) \(-30092621520062500000\) \([]\) \(1451520\) \(2.4436\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 41650.e1 has rank \(2\).

Complex multiplication

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

Modular form 41650.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} - 2 q^{3} + q^{4} + 2 q^{6} - q^{8} + q^{9} - 5 q^{11} - 2 q^{12} - q^{13} + q^{16} + q^{17} - q^{18} + 3 q^{19} + O(q^{20})\) Copy content Toggle raw display