# Properties

 Label 169050.hu Number of curves $2$ Conductor $169050$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("hu1")

sage: E.isogeny_class()

## Elliptic curves in class 169050.hu

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
169050.hu1 169050bg1 $$[1, 0, 0, -28813, -1040383]$$ $$1439069689/579600$$ $$1065458756250000$$ $$[2]$$ $$884736$$ $$1.5815$$ $$\Gamma_0(N)$$-optimal
169050.hu2 169050bg2 $$[1, 0, 0, 93687, -7532883]$$ $$49471280711/41992020$$ $$-77192486890312500$$ $$[2]$$ $$1769472$$ $$1.9281$$

## Rank

sage: E.rank()

The elliptic curves in class 169050.hu have rank $$1$$.

## Complex multiplication

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

## Modular form 169050.2.a.hu

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{6} + q^{8} + q^{9} - 2q^{11} + q^{12} + 4q^{13} + q^{16} - 6q^{17} + q^{18} + 4q^{19} + O(q^{20})$$

## 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 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.