# Properties

 Label 8550.t Number of curves $4$ Conductor $8550$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("8550.t1")

sage: E.isogeny_class()

## Elliptic curves in class 8550.t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
8550.t1 8550ba3 [1, -1, 1, -684005, -217568253]  73728
8550.t2 8550ba4 [1, -1, 1, -49505, -2243253]  73728
8550.t3 8550ba2 [1, -1, 1, -42755, -3390753] [2, 2] 36864
8550.t4 8550ba1 [1, -1, 1, -2255, -69753]  18432 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 8550.t have rank $$1$$.

## Modular form8550.2.a.t

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 