# Properties

 Label 537.a Number of curves 2 Conductor 537 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("537.a1")
sage: E.isogeny_class()

## Elliptic curves in class 537.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
537.a1 537e1 [0, 1, 1, -340, 2308] 5 192 $$\Gamma_0(N)$$-optimal
537.a2 537e2 [0, 1, 1, 2450, -39812] 1 960

## Rank

sage: E.rank()

The elliptic curves in class 537.a have rank $$0$$.

## Modular form537.2.a.a

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

## Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the LMFDB numbering.

$$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels.