# Properties

 Label 236691o Number of curves $2$ Conductor $236691$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("o1")

sage: E.isogeny_class()

## Elliptic curves in class 236691o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
236691.o1 236691o1 $$[1, -1, 0, -1183509, -495012056]$$ $$10418796526321/6390657$$ $$112451839809475257$$ $$$$ $$5160960$$ $$2.2146$$ $$\Gamma_0(N)$$-optimal
236691.o2 236691o2 $$[1, -1, 0, -962424, -685808411]$$ $$-5602762882081/8312741073$$ $$-146273384335701550473$$ $$$$ $$10321920$$ $$2.5611$$

## Rank

sage: E.rank()

The elliptic curves in class 236691o have rank $$1$$.

## Complex multiplication

The elliptic curves in class 236691o do not have complex multiplication.

## Modular form 236691.2.a.o

sage: E.q_eigenform(10)

$$q + q^{2} - q^{4} - 4q^{5} - q^{7} - 3q^{8} - 4q^{10} - 4q^{11} + q^{13} - q^{14} - q^{16} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 