# Properties

 Label 61710bo Number of curves $2$ Conductor $61710$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 61710bo

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
61710.bs2 61710bo1 [1, 1, 1, 3204, -59751] [2] 122880 $$\Gamma_0(N)$$-optimal
61710.bs1 61710bo2 [1, 1, 1, -17366, -569887] [2] 245760

## Rank

sage: E.rank()

The elliptic curves in class 61710bo have rank $$1$$.

## Complex multiplication

The elliptic curves in class 61710bo do not have complex multiplication.

## Modular form 61710.2.a.bo

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} + 2q^{7} + q^{8} + q^{9} - q^{10} - q^{12} + 2q^{14} + q^{15} + q^{16} - q^{17} + q^{18} + O(q^{20})$$

## 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.