Properties

Label 10002.e
Number of curves 1
Conductor 10002
CM no
Rank 1

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Show commands for: SageMath
sage: E = EllipticCurve("10002.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 10002.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
10002.e1 10002e1 [1, 0, 0, -37, -7] [] 2160 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 10002.e1 has rank \(1\).

Modular form 10002.2.a.e

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