# Properties

 Label 33600em Number of curves 6 Conductor 33600 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("33600.ce1")

sage: E.isogeny_class()

## Elliptic curves in class 33600em

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33600.ce6 33600em1 [0, -1, 0, 1567, 4737] [2] 32768 $$\Gamma_0(N)$$-optimal
33600.ce5 33600em2 [0, -1, 0, -6433, 44737] [2, 2] 65536
33600.ce3 33600em3 [0, -1, 0, -62433, -5947263] [2] 131072
33600.ce2 33600em4 [0, -1, 0, -78433, 8468737] [2, 2] 131072
33600.ce4 33600em5 [0, -1, 0, -54433, 13724737] [2] 262144
33600.ce1 33600em6 [0, -1, 0, -1254433, 541196737] [2] 262144

## Rank

sage: E.rank()

The elliptic curves in class 33600em have rank $$0$$.

## Modular form 33600.2.a.ce

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.