Properties

Label 8041.a
Number of curves 1
Conductor 8041
CM no
Rank 1

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Show commands for: SageMath
sage: E = EllipticCurve("8041.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8041.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
8041.a1 8041b1 [0, 1, 1, -1072, -14872] [] 9144 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 8041.a1 has rank \(1\).

Modular form 8041.2.a.a

sage: E.q_eigenform(10)
 
\( q - 2q^{2} - 2q^{3} + 2q^{4} + 2q^{5} + 4q^{6} + 3q^{7} + q^{9} - 4q^{10} + q^{11} - 4q^{12} - 2q^{13} - 6q^{14} - 4q^{15} - 4q^{16} + q^{17} - 2q^{18} - 8q^{19} + O(q^{20}) \)