Properties

Label 51870.f
Number of curves 1
Conductor 51870
CM no
Rank 1

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Show commands for: SageMath

sage: E = EllipticCurve("51870.f1")
sage: E.isogeny_class()

Elliptic curves in class 51870.f

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
51870.f1 51870i1 [1, 1, 0, -162858, -343886508] 1 2534400 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curve 51870.f1 has rank \(1\).

Modular form None

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