# Properties

 Label 53040cq Number of curves 2 Conductor 53040 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("53040.cx1")

sage: E.isogeny_class()

## Elliptic curves in class 53040cq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
53040.cx1 53040cq1 [0, 1, 0, -217920, -38781900]  368640 $$\Gamma_0(N)$$-optimal
53040.cx2 53040cq2 [0, 1, 0, -33600, -102114252]  737280

## Rank

sage: E.rank()

The elliptic curves in class 53040cq have rank $$0$$.

## Modular form 53040.2.a.cx

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} + 2q^{7} + q^{9} - q^{13} + q^{15} - q^{17} - 2q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 