# Properties

 Label 206910.eo Number of curves $4$ Conductor $206910$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("206910.eo1")

sage: E.isogeny_class()

## Elliptic curves in class 206910.eo

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
206910.eo1 206910q4 [1, -1, 1, -676292, -213586491]  2621440
206910.eo2 206910q2 [1, -1, 1, -55562, -1048539] [2, 2] 1310720
206910.eo3 206910q1 [1, -1, 1, -33782, 2383989]  655360 $$\Gamma_0(N)$$-optimal
206910.eo4 206910q3 [1, -1, 1, 216688, -8453739]  2621440

## Rank

sage: E.rank()

The elliptic curves in class 206910.eo have rank $$0$$.

## Modular form 206910.2.a.eo

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{5} + q^{8} + q^{10} - 2q^{13} + q^{16} + 2q^{17} + q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 