# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("fy1")

sage: E.isogeny_class()

## Elliptic curves in class 139650.fy

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
139650.fy1 139650ek1 $$[1, 1, 1, -493438, 133207031]$$ $$2479176213198607/541500$$ $$2902101562500$$ $$$$ $$1105920$$ $$1.7751$$ $$\Gamma_0(N)$$-optimal
139650.fy2 139650ek2 $$[1, 1, 1, -491688, 134201031]$$ $$-2452892123873647/36652781250$$ $$-196435999511718750$$ $$$$ $$2211840$$ $$2.1217$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 139650.2.a.fy

sage: E.q_eigenform(10)

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