# Properties

 Label 9680t Number of curves 4 Conductor 9680 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("9680.ba1")

sage: E.isogeny_class()

## Elliptic curves in class 9680t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9680.ba3 9680t1 [0, -1, 0, -161, 596]  2880 $$\Gamma_0(N)$$-optimal
9680.ba4 9680t2 [0, -1, 0, 444, 3500]  5760
9680.ba1 9680t3 [0, -1, 0, -5001, -134440]  8640
9680.ba2 9680t4 [0, -1, 0, -4396, -168804]  17280

## Rank

sage: E.rank()

The elliptic curves in class 9680t have rank $$1$$.

## Modular form9680.2.a.ba

sage: E.q_eigenform(10)

$$q + 2q^{3} - q^{5} + 2q^{7} + q^{9} - 2q^{13} - 2q^{15} + 6q^{17} - 4q^{19} + O(q^{20})$$

## 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. 