# Properties

 Label 52800eg Number of curves 4 Conductor 52800 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("52800.cv1")

sage: E.isogeny_class()

## Elliptic curves in class 52800eg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
52800.cv3 52800eg1 [0, -1, 0, -8833, -298463]  110592 $$\Gamma_0(N)$$-optimal
52800.cv4 52800eg2 [0, -1, 0, 7167, -1274463]  221184
52800.cv1 52800eg3 [0, -1, 0, -128833, 17773537]  331776
52800.cv2 52800eg4 [0, -1, 0, -64833, 35373537]  663552

## Rank

sage: E.rank()

The elliptic curves in class 52800eg have rank $$0$$.

## Modular form 52800.2.a.cv

sage: E.q_eigenform(10)

$$q - q^{3} + 2q^{7} + q^{9} - q^{11} - 4q^{13} + 6q^{17} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 