# Properties

 Label 169050.hx Number of curves $4$ Conductor $169050$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("hx1")

sage: E.isogeny_class()

## Elliptic curves in class 169050.hx

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
169050.hx1 169050bh4 $$[1, 0, 0, -3692956688, -237272203008]$$ $$3029968325354577848895529/1753440696000000000000$$ $$3223289756932875000000000000000$$ $$[2]$$ $$318504960$$ $$4.5435$$
169050.hx2 169050bh2 $$[1, 0, 0, -2540458313, -49285104061383]$$ $$986396822567235411402169/6336721794060000$$ $$11648577849208827187500000$$ $$[2]$$ $$106168320$$ $$3.9942$$
169050.hx3 169050bh1 $$[1, 0, 0, -155726313, -801117769383]$$ $$-227196402372228188089/19338934824115200$$ $$-35550099111286393200000000$$ $$[2]$$ $$53084160$$ $$3.6476$$ $$\Gamma_0(N)$$-optimal
169050.hx4 169050bh3 $$[1, 0, 0, 923235312, -29543563008]$$ $$47342661265381757089751/27397579603968000000$$ $$-50364028794175488000000000000$$ $$[2]$$ $$159252480$$ $$4.1969$$

## Rank

sage: E.rank()

The elliptic curves in class 169050.hx have rank $$0$$.

## Complex multiplication

The elliptic curves in class 169050.hx do not have complex multiplication.

## Modular form 169050.2.a.hx

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{6} + q^{8} + q^{9} + q^{12} - 4q^{13} + q^{16} + q^{18} - 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.