# Properties

 Label 27200z Number of curves 4 Conductor 27200 CM no Rank 0 Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("27200.p1")

sage: E.isogeny_class()

## Elliptic curves in class 27200z

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
27200.p4 27200z1 [0, 1, 0, -4833, 78463] [2] 55296 $$\Gamma_0(N)$$-optimal
27200.p3 27200z2 [0, 1, 0, -68833, 6926463] [2] 110592
27200.p2 27200z3 [0, 1, 0, -164833, -25809537] [2] 165888
27200.p1 27200z4 [0, 1, 0, -180833, -20513537] [2] 331776

## Rank

sage: E.rank()

The elliptic curves in class 27200z have rank $$0$$.

## Modular form 27200.2.a.p

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.