Properties

Label 61.a
Number of curves 1
Conductor 61
CM no
Rank 1

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Show commands for: SageMath

sage: E = EllipticCurve("61.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 61.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
61.a1 61a1 [1, 0, 0, -2, 1] [] 2 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 61.a1 has rank \(1\).

Modular form 61.2.a.a

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