# Properties

 Label 33600.eo Number of curves $8$ Conductor $33600$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("33600.eo1")

sage: E.isogeny_class()

## Elliptic curves in class 33600.eo

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33600.eo1 33600cc8 [0, 1, 0, -10321633, 8026548863] [2] 2654208
33600.eo2 33600cc5 [0, 1, 0, -9217633, 10768452863] [2] 884736
33600.eo3 33600cc6 [0, 1, 0, -4321633, -3367451137] [2, 2] 1327104
33600.eo4 33600cc3 [0, 1, 0, -4289633, -3421051137] [2] 663552
33600.eo5 33600cc2 [0, 1, 0, -577633, 167172863] [2, 2] 442368
33600.eo6 33600cc4 [0, 1, 0, -129633, 420292863] [2] 884736
33600.eo7 33600cc1 [0, 1, 0, -65633, -2299137] [2] 221184 $$\Gamma_0(N)$$-optimal
33600.eo8 33600cc7 [0, 1, 0, 1166367, -11330539137] [2] 2654208

## Rank

sage: E.rank()

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

## Modular form 33600.2.a.eo

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrrrrrr} 1 & 3 & 2 & 4 & 6 & 12 & 12 & 4 \\ 3 & 1 & 6 & 12 & 2 & 4 & 4 & 12 \\ 2 & 6 & 1 & 2 & 3 & 6 & 6 & 2 \\ 4 & 12 & 2 & 1 & 6 & 12 & 3 & 4 \\ 6 & 2 & 3 & 6 & 1 & 2 & 2 & 6 \\ 12 & 4 & 6 & 12 & 2 & 1 & 4 & 3 \\ 12 & 4 & 6 & 3 & 2 & 4 & 1 & 12 \\ 4 & 12 & 2 & 4 & 6 & 3 & 12 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.