# Properties

 Label 9702.bo Number of curves $2$ Conductor $9702$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 9702.bo

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9702.bo1 9702bt2 $$[1, -1, 1, -31869095, 69255238511]$$ $$121681065322255375/12702096$$ $$373667459353938288$$ $$$$ $$458752$$ $$2.8008$$
9702.bo2 9702bt1 $$[1, -1, 1, -1986935, 1088055119]$$ $$-29489309167375/303595776$$ $$-8931113596410179328$$ $$$$ $$229376$$ $$2.4542$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 9702.bo have rank $$0$$.

## Complex multiplication

The elliptic curves in class 9702.bo do not have complex multiplication.

## Modular form9702.2.a.bo

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 