Properties

Label 31814a
Number of curves 1
Conductor 31814
CM no
Rank 3

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Show commands for: SageMath
sage: E = EllipticCurve("31814.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 31814a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
31814.a1 31814a1 [1, 0, 1, 2, 12] [] 5808 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 31814a1 has rank \(3\).

Modular form 31814.2.a.a

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