# Properties

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

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 8550.t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8550.t1 8550ba3 $$[1, -1, 1, -684005, -217568253]$$ $$3107086841064961/570$$ $$6492656250$$ $$[2]$$ $$73728$$ $$1.7185$$
8550.t2 8550ba4 $$[1, -1, 1, -49505, -2243253]$$ $$1177918188481/488703750$$ $$5566641152343750$$ $$[2]$$ $$73728$$ $$1.7185$$
8550.t3 8550ba2 $$[1, -1, 1, -42755, -3390753]$$ $$758800078561/324900$$ $$3700814062500$$ $$[2, 2]$$ $$36864$$ $$1.3720$$
8550.t4 8550ba1 $$[1, -1, 1, -2255, -69753]$$ $$-111284641/123120$$ $$-1402413750000$$ $$[2]$$ $$18432$$ $$1.0254$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 8550.t do not have complex multiplication.

## Modular form8550.2.a.t

sage: E.q_eigenform(10)

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

## 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.