# Properties

 Label 133584.dd Number of curves 2 Conductor 133584 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("133584.dd1")

sage: E.isogeny_class()

## Elliptic curves in class 133584.dd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
133584.dd1 133584v2 [0, 1, 0, -2396808, -1417918284] [2] 2457600
133584.dd2 133584v1 [0, 1, 0, -44568, -52678188] [2] 1228800 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 133584.dd have rank $$0$$.

## Modular form 133584.2.a.dd

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.