# Properties

 Label 83790bo Number of curves $4$ Conductor $83790$ CM no Rank $2$ Graph

# Learn more

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

sage: E.isogeny_class()

## Elliptic curves in class 83790bo

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
83790.d3 83790bo1 $$[1, -1, 0, -13680, 615600]$$ $$3301293169/22800$$ $$1955467558800$$ $$[2]$$ $$196608$$ $$1.1920$$ $$\Gamma_0(N)$$-optimal
83790.d2 83790bo2 $$[1, -1, 0, -22500, -268164]$$ $$14688124849/8122500$$ $$696635317822500$$ $$[2, 2]$$ $$393216$$ $$1.5386$$
83790.d4 83790bo3 $$[1, -1, 0, 87750, -2186514]$$ $$871257511151/527800050$$ $$-45267362952106050$$ $$[2]$$ $$786432$$ $$1.8852$$
83790.d1 83790bo4 $$[1, -1, 0, -273870, -55016550]$$ $$26487576322129/44531250$$ $$3819272575781250$$ $$[2]$$ $$786432$$ $$1.8852$$

## Rank

sage: E.rank()

The elliptic curves in class 83790bo have rank $$2$$.

## Complex multiplication

The elliptic curves in class 83790bo do not have complex multiplication.

## Modular form 83790.2.a.bo

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} - 4q^{11} - 2q^{13} + q^{16} + 2q^{17} + q^{19} + O(q^{20})$$

## 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 Cremona 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 Cremona labels.