# Properties

 Label 139650.jf Number of curves $4$ Conductor $139650$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("jf1")

sage: E.isogeny_class()

## Elliptic curves in class 139650.jf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
139650.jf1 139650cm4 $$[1, 0, 0, -2173368688, -38998644440008]$$ $$617611911727813844500009/1197723879765000$$ $$2201734636413632578125000$$ $$[2]$$ $$74317824$$ $$3.9244$$
139650.jf2 139650cm3 $$[1, 0, 0, -365366688, 1897487521992]$$ $$2934284984699764805929/851931751022747640$$ $$1566076852751175579661875000$$ $$[2]$$ $$74317824$$ $$3.9244$$
139650.jf3 139650cm2 $$[1, 0, 0, -137271688, -595818923008]$$ $$155617476551393929129/6633105589454400$$ $$12193409992089386025000000$$ $$[2, 2]$$ $$37158912$$ $$3.5778$$
139650.jf4 139650cm1 $$[1, 0, 0, 4240312, -34723843008]$$ $$4586790226340951/286015269335040$$ $$-525772037843720640000000$$ $$[2]$$ $$18579456$$ $$3.2312$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 139650.2.a.jf

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.