# Properties

 Label 13200ck Number of curves 4 Conductor 13200 CM no Rank 0 Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("13200.cp1")

sage: E.isogeny_class()

## Elliptic curves in class 13200ck

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
13200.cp3 13200ck1 [0, 1, 0, -2208, -38412] [2] 13824 $$\Gamma_0(N)$$-optimal
13200.cp4 13200ck2 [0, 1, 0, 1792, -158412] [2] 27648
13200.cp1 13200ck3 [0, 1, 0, -32208, 2205588] [2] 41472
13200.cp2 13200ck4 [0, 1, 0, -16208, 4413588] [2] 82944

## Rank

sage: E.rank()

The elliptic curves in class 13200ck have rank $$0$$.

## Modular form 13200.2.a.cp

sage: E.q_eigenform(10)

$$q + q^{3} + 2q^{7} + q^{9} + q^{11} + 4q^{13} + 6q^{17} + 4q^{19} + O(q^{20})$$

## 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.