# Properties

 Label 52800.ex Number of curves 4 Conductor 52800 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("52800.ex1")

sage: E.isogeny_class()

## Elliptic curves in class 52800.ex

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
52800.ex1 52800db3 [0, 1, 0, -128833, -17773537]  331776
52800.ex2 52800db4 [0, 1, 0, -64833, -35373537]  663552
52800.ex3 52800db1 [0, 1, 0, -8833, 298463]  110592 $$\Gamma_0(N)$$-optimal
52800.ex4 52800db2 [0, 1, 0, 7167, 1274463]  221184

## Rank

sage: E.rank()

The elliptic curves in class 52800.ex have rank $$1$$.

## Modular form 52800.2.a.ex

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 LMFDB 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 LMFDB labels. 