# Properties

 Label 9680bc Number of curves $4$ Conductor $9680$ CM no Rank $0$ Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("bc1")

sage: E.isogeny_class()

## Elliptic curves in class 9680bc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9680.bb4 9680bc1 [0, -1, 0, -5485, 154992] [2] 17280 $$\Gamma_0(N)$$-optimal
9680.bb3 9680bc2 [0, -1, 0, -12140, -286900] [2] 34560
9680.bb2 9680bc3 [0, -1, 0, -53885, -4735828] [2] 51840
9680.bb1 9680bc4 [0, -1, 0, -859140, -306223300] [2] 103680

## Rank

sage: E.rank()

The elliptic curves in class 9680bc have rank $$0$$.

## Complex multiplication

The elliptic curves in class 9680bc do not have complex multiplication.

## Modular form9680.2.a.bc

sage: E.q_eigenform(10)

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

## 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.