# Properties

 Label 33600.dy Number of curves $4$ Conductor $33600$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("dy1")

sage: E.isogeny_class()

## Elliptic curves in class 33600.dy

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33600.dy1 33600gh4 [0, 1, 0, -597633, -178027137] [2] 294912
33600.dy2 33600gh2 [0, 1, 0, -37633, -2747137] [2, 2] 147456
33600.dy3 33600gh1 [0, 1, 0, -5633, 100863] [2] 73728 $$\Gamma_0(N)$$-optimal
33600.dy4 33600gh3 [0, 1, 0, 10367, -9227137] [2] 294912

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 33600.2.a.dy

sage: E.q_eigenform(10)

$$q + q^{3} - q^{7} + q^{9} - 4q^{11} - 2q^{13} + 6q^{17} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.