# Properties

 Label 33600gy Number of curves $4$ Conductor $33600$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("gy1")

sage: E.isogeny_class()

## Elliptic curves in class 33600gy

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33600.fi4 33600gy1 $$[0, 1, 0, -40003908, -96203669562]$$ $$7079962908642659949376/100085966990454375$$ $$100085966990454375000000$$ $$[2]$$ $$5160960$$ $$3.2181$$ $$\Gamma_0(N)$$-optimal
33600.fi2 33600gy2 $$[0, 1, 0, -637875033, -6201065726937]$$ $$448487713888272974160064/91549016015625$$ $$5859137025000000000000$$ $$[2, 2]$$ $$10321920$$ $$3.5647$$
33600.fi3 33600gy3 $$[0, 1, 0, -635688033, -6245695835937]$$ $$-55486311952875723077768/801237030029296875$$ $$-410233359375000000000000000$$ $$[2]$$ $$20643840$$ $$3.9113$$
33600.fi1 33600gy4 $$[0, 1, 0, -10206000033, -396858041351937]$$ $$229625675762164624948320008/9568125$$ $$4898880000000000$$ $$[2]$$ $$20643840$$ $$3.9113$$

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 33600gy do not have complex multiplication.

## Modular form 33600.2.a.gy

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.