# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("33600.dx1")

sage: E.isogeny_class()

## Elliptic curves in class 33600gg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33600.dx4 33600gg1 [0, 1, 0, -17533, -899437] [2] 49152 $$\Gamma_0(N)$$-optimal
33600.dx3 33600gg2 [0, 1, 0, -18033, -845937] [2, 2] 98304
33600.dx5 33600gg3 [0, 1, 0, 23967, -4163937] [2] 196608
33600.dx2 33600gg4 [0, 1, 0, -68033, 5904063] [2, 2] 196608
33600.dx6 33600gg5 [0, 1, 0, 111967, 32004063] [2] 393216
33600.dx1 33600gg6 [0, 1, 0, -1048033, 412604063] [4] 393216

## Rank

sage: E.rank()

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

## Modular form 33600.2.a.dx

sage: E.q_eigenform(10)

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

## 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.