# Properties

 Label 20160.dk Number of curves $8$ Conductor $20160$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("20160.dk1")

sage: E.isogeny_class()

## Elliptic curves in class 20160.dk

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
20160.dk1 20160en7 [0, 0, 0, -202309932, -1107576977456] [2] 1769472
20160.dk2 20160en6 [0, 0, 0, -12644652, -17305081904] [2, 2] 884736
20160.dk3 20160en8 [0, 0, 0, -11723052, -19934591024] [2] 1769472
20160.dk4 20160en4 [0, 0, 0, -2509932, -1503617456] [2] 589824
20160.dk5 20160en3 [0, 0, 0, -848172, -228497456] [2] 442368
20160.dk6 20160en2 [0, 0, 0, -332652, 38767696] [2, 2] 294912
20160.dk7 20160en1 [0, 0, 0, -286572, 59024464] [2] 147456 $$\Gamma_0(N)$$-optimal
20160.dk8 20160en5 [0, 0, 0, 1107348, 284719696] [2] 589824

## Rank

sage: E.rank()

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

## Modular form 20160.2.a.dk

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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.