Properties

Label 129.a
Number of curves 1
Conductor 129
CM no
Rank 1

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Show commands for: SageMath
sage: E = EllipticCurve("129.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 129.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
129.a1 129a1 [0, -1, 1, -19, 39] [] 8 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 129.a1 has rank \(1\).

Modular form 129.2.a.a

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