# Properties

 Label 20160cg Number of curves 8 Conductor 20160 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("20160.et1")

sage: E.isogeny_class()

## Elliptic curves in class 20160cg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
20160.et7 20160cg1 [0, 0, 0, -286572, -59024464] [2] 147456 $$\Gamma_0(N)$$-optimal
20160.et6 20160cg2 [0, 0, 0, -332652, -38767696] [2, 2] 294912
20160.et5 20160cg3 [0, 0, 0, -848172, 228497456] [2] 442368
20160.et4 20160cg4 [0, 0, 0, -2509932, 1503617456] [2] 589824
20160.et8 20160cg5 [0, 0, 0, 1107348, -284719696] [2] 589824
20160.et2 20160cg6 [0, 0, 0, -12644652, 17305081904] [2, 2] 884736
20160.et1 20160cg7 [0, 0, 0, -202309932, 1107576977456] [2] 1769472
20160.et3 20160cg8 [0, 0, 0, -11723052, 19934591024] [2] 1769472

## Rank

sage: E.rank()

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

## Modular form 20160.2.a.et

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.