# Properties

 Label 15680cp Number of curves 4 Conductor 15680 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("15680.de1")

sage: E.isogeny_class()

## Elliptic curves in class 15680cp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
15680.de3 15680cp1 [0, -1, 0, -261, 1205]  5760 $$\Gamma_0(N)$$-optimal
15680.de4 15680cp2 [0, -1, 0, 719, 7281]  11520
15680.de1 15680cp3 [0, -1, 0, -8101, -277899]  17280
15680.de2 15680cp4 [0, -1, 0, -7121, -348655]  34560

## Rank

sage: E.rank()

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

## Modular form 15680.2.a.de

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. 