# Properties

 Label 106560.ex Number of curves $6$ Conductor $106560$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("106560.ex1")

sage: E.isogeny_class()

## Elliptic curves in class 106560.ex

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
106560.ex1 106560fo4 [0, 0, 0, -196418892, 1059553759376] [2] 10616832
106560.ex2 106560fo6 [0, 0, 0, -174600012, -884142545776] [2] 21233664
106560.ex3 106560fo3 [0, 0, 0, -16891212, 3000995984] [2, 2] 10616832
106560.ex4 106560fo2 [0, 0, 0, -12283212, 16535613584] [2, 2] 5308416
106560.ex5 106560fo1 [0, 0, 0, -486732, 449933456] [2] 2654208 $$\Gamma_0(N)$$-optimal
106560.ex6 106560fo5 [0, 0, 0, 67089588, 23929011344] [2] 21233664

## Rank

sage: E.rank()

The elliptic curves in class 106560.ex have rank $$0$$.

## Modular form 106560.2.a.ex

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.