# Properties

 Label 43.a Number of curves 1 Conductor $43$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("43.a1")
sage: E.isogeny_class()

## Elliptic curves in class 43.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
43.a1 43a1 [0, 1, 1, 0, 0] 1 2 $\Gamma_0(N)$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 43.a have rank $1$.

## Modular form43.2.1.a

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