# Properties

 Label 166410.ct Number of curves $2$ Conductor $166410$ CM no Rank $0$ Graph # Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("ct1")

sage: E.isogeny_class()

## Elliptic curves in class 166410.ct

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
166410.ct1 166410f2 $$[1, -1, 1, -29621327, 72605965079]$$ $$-337335507529/72000000$$ $$-613490256170721288000000$$ $$$$ $$24966144$$ $$3.2858$$
166410.ct2 166410f1 $$[1, -1, 1, 2579008, -578956309]$$ $$222641831/145800$$ $$-1242317768745710608200$$ $$[]$$ $$8322048$$ $$2.7364$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 166410.ct have rank $$0$$.

## Complex multiplication

The elliptic curves in class 166410.ct do not have complex multiplication.

## Modular form 166410.2.a.ct

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{5} + 2q^{7} + q^{8} + q^{10} + 3q^{11} - 4q^{13} + 2q^{14} + q^{16} + 3q^{17} - q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 