Properties

Label 71058.e
Number of curves 1
Conductor 71058
CM no
Rank 1

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Show commands for: SageMath
sage: E = EllipticCurve("71058.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 71058.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
71058.e1 71058e1 [1, 0, 1, -8925, 306040] [] 179712 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 71058.e1 has rank \(1\).

Modular form 71058.2.a.e

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