# Properties

 Label 20160.cp Number of curves $4$ Conductor $20160$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cp1")

sage: E.isogeny_class()

## Elliptic curves in class 20160.cp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
20160.cp1 20160ee3 [0, 0, 0, -215148, 38410832] [2] 98304
20160.cp2 20160ee2 [0, 0, 0, -13548, 590672] [2, 2] 49152
20160.cp3 20160ee1 [0, 0, 0, -2028, -22192] [2] 24576 $$\Gamma_0(N)$$-optimal
20160.cp4 20160ee4 [0, 0, 0, 3732, 1993808] [2] 98304

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 20160.cp do not have complex multiplication.

## Modular form 20160.2.a.cp

sage: E.q_eigenform(10)

$$q - q^{5} + q^{7} + 4q^{11} + 2q^{13} + 6q^{17} + O(q^{20})$$

## 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.