# Properties

 Label 169050.a Number of curves $2$ Conductor $169050$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

## Elliptic curves in class 169050.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
169050.a1 169050hy1 $$[1, 1, 0, -300150, -60547500]$$ $$1626794704081/83462400$$ $$153426060900000000$$ $$$$ $$3538944$$ $$2.0555$$ $$\Gamma_0(N)$$-optimal
169050.a2 169050hy2 $$[1, 1, 0, 189850, -238417500]$$ $$411664745519/13605414480$$ $$-25010365752461250000$$ $$$$ $$7077888$$ $$2.4021$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 169050.2.a.a

sage: E.q_eigenform(10)

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