# Properties

 Label 33600.dp Number of curves $6$ Conductor $33600$ CM no Rank $0$ Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("33600.dp1")

sage: E.isogeny_class()

## Elliptic curves in class 33600.dp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33600.dp1 33600x6 [0, -1, 0, -1048033, -412604063] [2] 393216
33600.dp2 33600x4 [0, -1, 0, -68033, -5904063] [2, 2] 196608
33600.dp3 33600x2 [0, -1, 0, -18033, 845937] [2, 2] 98304
33600.dp4 33600x1 [0, -1, 0, -17533, 899437] [2] 49152 $$\Gamma_0(N)$$-optimal
33600.dp5 33600x3 [0, -1, 0, 23967, 4163937] [2] 196608
33600.dp6 33600x5 [0, -1, 0, 111967, -32004063] [4] 393216

## Rank

sage: E.rank()

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

## Modular form 33600.2.a.dp

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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.