# Properties

 Label 20160.dp Number of curves 4 Conductor 20160 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("20160.dp1")

sage: E.isogeny_class()

## Elliptic curves in class 20160.dp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
20160.dp1 20160eo3 [0, 0, 0, -64812, -6350384]  65536
20160.dp2 20160eo2 [0, 0, 0, -4332, -84656] [2, 2] 32768
20160.dp3 20160eo1 [0, 0, 0, -1452, 20176]  16384 $$\Gamma_0(N)$$-optimal
20160.dp4 20160eo4 [0, 0, 0, 10068, -528176]  65536

## Rank

sage: E.rank()

The elliptic curves in class 20160.dp have rank $$0$$.

## Modular form 20160.2.a.dp

sage: E.q_eigenform(10)

$$q + q^{5} - q^{7} + 6q^{13} - 2q^{17} - 8q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 