# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("83790.d1")

sage: E.isogeny_class()

## Elliptic curves in class 83790bo

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
83790.d3 83790bo1 [1, -1, 0, -13680, 615600]  196608 $$\Gamma_0(N)$$-optimal
83790.d2 83790bo2 [1, -1, 0, -22500, -268164] [2, 2] 393216
83790.d4 83790bo3 [1, -1, 0, 87750, -2186514]  786432
83790.d1 83790bo4 [1, -1, 0, -273870, -55016550]  786432

## Rank

sage: E.rank()

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

## Modular form 83790.2.a.d

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. 