# Properties

 Label 28560cf Number of curves 4 Conductor 28560 CM no Rank 2 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("28560.e1")

sage: E.isogeny_class()

## Elliptic curves in class 28560cf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
28560.e4 28560cf1 [0, -1, 0, 224, -2240]  16384 $$\Gamma_0(N)$$-optimal
28560.e3 28560cf2 [0, -1, 0, -1776, -23040] [2, 2] 32768
28560.e2 28560cf3 [0, -1, 0, -8576, 287040]  65536
28560.e1 28560cf4 [0, -1, 0, -26976, -1696320]  65536

## Rank

sage: E.rank()

The elliptic curves in class 28560cf have rank $$2$$.

## Modular form 28560.2.a.e

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} - q^{7} + q^{9} - 6q^{13} + q^{15} - q^{17} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 