# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("61.a1")
sage: E.isogeny_class()

## Elliptic curves in class 61a

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

## Rank

sage: E.rank()

The elliptic curve 61a1 has rank $$1$$.

## Modular form61.2.a.a

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