# Properties

 Label 20160cr Number of curves $4$ Conductor $20160$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("20160.s1")

sage: E.isogeny_class()

## Elliptic curves in class 20160cr

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
20160.s3 20160cr1 [0, 0, 0, -2988, -55088]  18432 $$\Gamma_0(N)$$-optimal
20160.s4 20160cr2 [0, 0, 0, 4692, -291632]  36864
20160.s1 20160cr3 [0, 0, 0, -60588, 5733072]  55296
20160.s2 20160cr4 [0, 0, 0, -43308, 9071568]  110592

## Rank

sage: E.rank()

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

## Modular form 20160.2.a.s

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 