# Properties

 Label 15680.cc Number of curves $4$ Conductor $15680$ CM no Rank $0$ Graph # Learn more

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

sage: E.isogeny_class()

## Elliptic curves in class 15680.cc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15680.cc1 15680dk3 $$[0, 0, 0, -20972, -1168944]$$ $$132304644/5$$ $$38551224320$$ $$$$ $$18432$$ $$1.1173$$
15680.cc2 15680dk2 $$[0, 0, 0, -1372, -16464]$$ $$148176/25$$ $$48189030400$$ $$[2, 2]$$ $$9216$$ $$0.77074$$
15680.cc3 15680dk1 $$[0, 0, 0, -392, 2744]$$ $$55296/5$$ $$602362880$$ $$$$ $$4608$$ $$0.42417$$ $$\Gamma_0(N)$$-optimal
15680.cc4 15680dk4 $$[0, 0, 0, 2548, -93296]$$ $$237276/625$$ $$-4818903040000$$ $$$$ $$18432$$ $$1.1173$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## 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 LMFDB 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 LMFDB labels. 