# Properties

 Label 15680cw Number of curves $2$ Conductor $15680$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cw1")

sage: E.isogeny_class()

## Elliptic curves in class 15680cw

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
15680.b1 15680cw1 [0, 0, 0, -8428, 297808] [] 23040 $$\Gamma_0(N)$$-optimal
15680.b2 15680cw2 [0, 0, 0, 58772, -2825648] [] 161280

## Rank

sage: E.rank()

The elliptic curves in class 15680cw have rank $$1$$.

## Complex multiplication

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

## Modular form 15680.2.a.cw

sage: E.q_eigenform(10)

$$q - 3q^{3} - q^{5} + 6q^{9} - 2q^{11} + 3q^{15} + 4q^{17} + 6q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.