# Properties

 Label 53550dt Number of curves $6$ Conductor $53550$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("53550.cs1")

sage: E.isogeny_class()

## Elliptic curves in class 53550dt

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
53550.cs5 53550dt1 [1, -1, 1, -15804905, -24150226903] [2] 3932160 $$\Gamma_0(N)$$-optimal
53550.cs4 53550dt2 [1, -1, 1, -20412905, -8916178903] [2, 2] 7864320
53550.cs6 53550dt3 [1, -1, 1, 78731095, -70187170903] [2] 15728640
53550.cs2 53550dt4 [1, -1, 1, -193284905, 1027278589097] [2, 2] 15728640
53550.cs3 53550dt5 [1, -1, 1, -65835905, 2361669619097] [2] 31457280
53550.cs1 53550dt6 [1, -1, 1, -3086685905, 66007278247097] [2] 31457280

## Rank

sage: E.rank()

The elliptic curves in class 53550dt have rank $$0$$.

## Modular form 53550.2.a.cs

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{7} + q^{8} - 4q^{11} + 2q^{13} - q^{14} + q^{16} + q^{17} + 4q^{19} + O(q^{20})$$

## 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.