# Properties

 Label 236992.bo Number of curves $4$ Conductor $236992$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("bo1")

sage: E.isogeny_class()

## Elliptic curves in class 236992.bo

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
236992.bo1 236992bo4 $$[0, 0, 0, -4187564, -3297549008]$$ $$209267191953/55223$$ $$2143023503310061568$$ $$$$ $$5406720$$ $$2.5018$$
236992.bo2 236992bo2 $$[0, 0, 0, -294124, -37961040]$$ $$72511713/25921$$ $$1005908991349620736$$ $$[2, 2]$$ $$2703360$$ $$2.1553$$
236992.bo3 236992bo1 $$[0, 0, 0, -124844, 16547120]$$ $$5545233/161$$ $$6247881933848576$$ $$$$ $$1351680$$ $$1.8087$$ $$\Gamma_0(N)$$-optimal
236992.bo4 236992bo3 $$[0, 0, 0, 890836, -266895312]$$ $$2014698447/1958887$$ $$-76017979489135624192$$ $$$$ $$5406720$$ $$2.5018$$

## Rank

sage: E.rank()

The elliptic curves in class 236992.bo have rank $$0$$.

## Complex multiplication

The elliptic curves in class 236992.bo do not have complex multiplication.

## Modular form 236992.2.a.bo

sage: E.q_eigenform(10)

$$q + 2q^{5} - q^{7} - 3q^{9} + 4q^{11} - 6q^{13} + 2q^{17} + 4q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 