# Properties

 Label 9702.bp Number of curves $2$ Conductor $9702$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("bp1")

E.isogeny_class()

## Elliptic curves in class 9702.bp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9702.bp1 9702cc2 $$[1, -1, 1, -199435865, 1068707030073]$$ $$10228636028672744397625/167006381634183168$$ $$14323489535009531322851328$$ $$[2]$$ $$3194880$$ $$3.6262$$
9702.bp2 9702cc1 $$[1, -1, 1, -738905, 46848304185]$$ $$-520203426765625/11054534935707648$$ $$-948104580894629358993408$$ $$[2]$$ $$1597440$$ $$3.2796$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 9702.bp have rank $$1$$.

## Complex multiplication

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

## Modular form9702.2.a.bp

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{8} + q^{11} - 6 q^{13} + q^{16} + 4 q^{17} - 6 q^{19} + O(q^{20})$$

## 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 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.