# Properties

 Label 10944.ck Number of curves $3$ Conductor $10944$ CM no Rank $0$ Graph # Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("ck1")

sage: E.isogeny_class()

## Elliptic curves in class 10944.ck

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10944.ck1 10944t3 $$[0, 0, 0, -27696, 1774082]$$ $$-50357871050752/19$$ $$-886464$$ $$[]$$ $$10368$$ $$0.92932$$
10944.ck2 10944t2 $$[0, 0, 0, -336, 2522]$$ $$-89915392/6859$$ $$-320013504$$ $$[]$$ $$3456$$ $$0.38001$$
10944.ck3 10944t1 $$[0, 0, 0, 24, 2]$$ $$32768/19$$ $$-886464$$ $$[]$$ $$1152$$ $$-0.16929$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 10944.ck have rank $$0$$.

## Complex multiplication

The elliptic curves in class 10944.ck do not have complex multiplication.

## Modular form 10944.2.a.ck

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 