# Properties

 Label 15680s Number of curves $4$ Conductor $15680$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("s1")

sage: E.isogeny_class()

## Elliptic curves in class 15680s

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
15680.n3 15680s1 [0, 1, 0, -261, -1205] [2] 5760 $$\Gamma_0(N)$$-optimal
15680.n4 15680s2 [0, 1, 0, 719, -7281] [2] 11520
15680.n1 15680s3 [0, 1, 0, -8101, 277899] [2] 17280
15680.n2 15680s4 [0, 1, 0, -7121, 348655] [2] 34560

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 15680.2.a.s

sage: E.q_eigenform(10)

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

## 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.