Properties

Label 61347.x
Number of curves 1
Conductor 61347
CM no
Rank 1

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Show commands for: SageMath
sage: E = EllipticCurve("61347.x1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 61347.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
61347.x1 61347y1 [1, 0, 1, 503, 25859] [] 63648 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 61347.x1 has rank \(1\).

Modular form 61347.2.a.x

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