# Properties

 Label 33600dd Number of curves 6 Conductor 33600 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("33600.fm1")

sage: E.isogeny_class()

## Elliptic curves in class 33600dd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33600.fm6 33600dd1 [0, 1, 0, 1567, -4737] [2] 32768 $$\Gamma_0(N)$$-optimal
33600.fm5 33600dd2 [0, 1, 0, -6433, -44737] [2, 2] 65536
33600.fm3 33600dd3 [0, 1, 0, -62433, 5947263] [2] 131072
33600.fm2 33600dd4 [0, 1, 0, -78433, -8468737] [2, 2] 131072
33600.fm4 33600dd5 [0, 1, 0, -54433, -13724737] [2] 262144
33600.fm1 33600dd6 [0, 1, 0, -1254433, -541196737] [2] 262144

## Rank

sage: E.rank()

The elliptic curves in class 33600dd have rank $$1$$.

## Modular form 33600.2.a.fm

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.