Properties

Label 31737.a
Number of curves 1
Conductor 31737
CM no
Rank 3

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Show commands for: SageMath
sage: E = EllipticCurve("31737.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 31737.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
31737.a1 31737a1 [0, -1, 1, -34, 90] [] 9408 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 31737.a1 has rank \(3\).

Modular form 31737.2.a.a

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