# Properties

 Label 15680ds Number of curves $2$ Conductor $15680$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ds1")

sage: E.isogeny_class()

## Elliptic curves in class 15680ds

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
15680.x2 15680ds1 [0, 1, 0, 7775, 291423] [2] 43008 $$\Gamma_0(N)$$-optimal
15680.x1 15680ds2 [0, 1, 0, -47105, 2782975] [2] 86016

## Rank

sage: E.rank()

The elliptic curves in class 15680ds have rank $$0$$.

## Complex multiplication

The elliptic curves in class 15680ds do not have complex multiplication.

## Modular form 15680.2.a.ds

sage: E.q_eigenform(10)

$$q - 2q^{3} + q^{5} + q^{9} + 4q^{11} + 2q^{13} - 2q^{15} - 2q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.