Properties

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

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

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.