# Properties

 Label 15680dk Number of curves 4 Conductor 15680 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("15680.cc1")

sage: E.isogeny_class()

## Elliptic curves in class 15680dk

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
15680.cc3 15680dk1 [0, 0, 0, -392, 2744]  4608 $$\Gamma_0(N)$$-optimal
15680.cc2 15680dk2 [0, 0, 0, -1372, -16464] [2, 2] 9216
15680.cc1 15680dk3 [0, 0, 0, -20972, -1168944]  18432
15680.cc4 15680dk4 [0, 0, 0, 2548, -93296]  18432

## Rank

sage: E.rank()

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

## Modular form 15680.2.a.cc

sage: E.q_eigenform(10)

$$q + q^{5} - 3q^{9} + 4q^{11} - 2q^{13} - 2q^{17} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 