# Properties

 Label 20160ev Number of curves $6$ Conductor $20160$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("20160.cy1")

sage: E.isogeny_class()

## Elliptic curves in class 20160ev

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
20160.cy6 20160ev1 [0, 0, 0, 5748, -234736] [2] 49152 $$\Gamma_0(N)$$-optimal
20160.cy5 20160ev2 [0, 0, 0, -40332, -2428144] [2, 2] 98304
20160.cy2 20160ev3 [0, 0, 0, -604812, -181029616] [2, 2] 196608
20160.cy4 20160ev4 [0, 0, 0, -213132, 35795216] [2] 196608
20160.cy1 20160ev5 [0, 0, 0, -9676812, -11586348016] [2] 393216
20160.cy3 20160ev6 [0, 0, 0, -564492, -206205424] [2] 393216

## Rank

sage: E.rank()

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

## Modular form 20160.2.a.cy

sage: E.q_eigenform(10)

$$q + q^{5} - q^{7} - 4q^{11} + 2q^{13} - 2q^{17} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.