Properties

Label 1006.e
Number of curves 1
Conductor 1006
CM no
Rank 1

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Show commands for: SageMath
sage: E = EllipticCurve("1006.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1006.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1006.e1 1006c1 [1, 0, 0, 5, 1] [] 96 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1006.e1 has rank \(1\).

Modular form 1006.2.a.e

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