# Properties

 Label 9702ca Number of curves 4 Conductor 9702 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("9702.bu1")

sage: E.isogeny_class()

## Elliptic curves in class 9702ca

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9702.bu3 9702ca1 [1, -1, 1, -2435, 44223]  11520 $$\Gamma_0(N)$$-optimal
9702.bu4 9702ca2 [1, -1, 1, 1975, 183579]  23040
9702.bu1 9702ca3 [1, -1, 1, -35510, -2556795]  34560
9702.bu2 9702ca4 [1, -1, 1, -17870, -5111067]  69120

## Rank

sage: E.rank()

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

## Modular form9702.2.a.bu

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 