Properties

Label 4002.k
Number of curves 1
Conductor 4002
CM no
Rank 1

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Show commands for: SageMath
sage: E = EllipticCurve("4002.k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4002.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4002.k1 4002h1 [1, 1, 1, 65, -91] [] 864 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4002.k1 has rank \(1\).

Modular form 4002.2.a.k

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