# Properties

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

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 206910.eo

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
206910.eo1 206910q4 $$[1, -1, 1, -676292, -213586491]$$ $$26487576322129/44531250$$ $$57510682994531250$$ $$[2]$$ $$2621440$$ $$2.1112$$
206910.eo2 206910q2 $$[1, -1, 1, -55562, -1048539]$$ $$14688124849/8122500$$ $$10489948578202500$$ $$[2, 2]$$ $$1310720$$ $$1.7646$$
206910.eo3 206910q1 $$[1, -1, 1, -33782, 2383989]$$ $$3301293169/22800$$ $$29445469693200$$ $$[2]$$ $$655360$$ $$1.4180$$ $$\Gamma_0(N)$$-optimal
206910.eo4 206910q3 $$[1, -1, 1, 216688, -8453739]$$ $$871257511151/527800050$$ $$-681636858611598450$$ $$[2]$$ $$2621440$$ $$2.1112$$

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 206910.eo do not have complex multiplication.

## 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.