# Properties

 Label 139650.hs Number of curves $2$ Conductor $139650$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("hs1")

sage: E.isogeny_class()

## Elliptic curves in class 139650.hs

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
139650.hs1 139650bo2 $$[1, 0, 0, -733188, 241576992]$$ $$23711636464489/363888$$ $$668922801750000$$ $$$$ $$1966080$$ $$1.9802$$
139650.hs2 139650bo1 $$[1, 0, 0, -47188, 3534992]$$ $$6321363049/715008$$ $$1314374628000000$$ $$$$ $$983040$$ $$1.6336$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 139650.hs have rank $$0$$.

## Complex multiplication

The elliptic curves in class 139650.hs do not have complex multiplication.

## Modular form 139650.2.a.hs

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 