Properties

Label 31478b
Number of curves 1
Conductor 31478
CM no
Rank 3

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Show commands for: SageMath

sage: E = EllipticCurve("31478.a1")
sage: E.isogeny_class()

Elliptic curves in class 31478b

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
31478.a1 31478b1 [1, 0, 1, -5, 12] 1 5536 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curve 31478b1 has rank \(3\).

Modular form 31478.2.a.a

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