# Properties

 Label 27200cl Number of curves 4 Conductor 27200 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("27200.ci1")

sage: E.isogeny_class()

## Elliptic curves in class 27200cl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
27200.ci4 27200cl1 [0, -1, 0, -4833, -78463] [2] 55296 $$\Gamma_0(N)$$-optimal
27200.ci3 27200cl2 [0, -1, 0, -68833, -6926463] [2] 110592
27200.ci2 27200cl3 [0, -1, 0, -164833, 25809537] [2] 165888
27200.ci1 27200cl4 [0, -1, 0, -180833, 20513537] [2] 331776

## Rank

sage: E.rank()

The elliptic curves in class 27200cl have rank $$1$$.

## Modular form 27200.2.a.ci

sage: E.q_eigenform(10)

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

## 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.