Properties

Label 139650.j
Number of curves $6$
Conductor $139650$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 139650.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
139650.j1 139650ip5 \([1, 1, 0, -4245421275, 106468732963125]\) \(4603390551972799451373601/3745967689800\) \(6886083636520003125000\) \([2]\) \(84934656\) \(3.9280\)  
139650.j2 139650ip3 \([1, 1, 0, -265396275, 1662734638125]\) \(1124604760397601117601/1013798336040000\) \(1863630631824530625000000\) \([2, 2]\) \(42467328\) \(3.5814\)  
139650.j3 139650ip6 \([1, 1, 0, -205371275, 2435076313125]\) \(-521116167586355661601/1092005739697609800\) \(-2007396613588813990003125000\) \([2]\) \(84934656\) \(3.9280\)  
139650.j4 139650ip4 \([1, 1, 0, -176804275, -895737249875]\) \(332501596620668284321/3896484375000000\) \(7162773284912109375000000\) \([2]\) \(42467328\) \(3.5814\)  
139650.j5 139650ip2 \([1, 1, 0, -20396275, 13149638125]\) \(510467451652317601/254721600000000\) \(468245961225000000000000\) \([2, 2]\) \(21233664\) \(3.2348\)  
139650.j6 139650ip1 \([1, 1, 0, 4691725, 1584070125]\) \(6213165856218719/4183818240000\) \(-7690969251840000000000\) \([2]\) \(10616832\) \(2.8882\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 139650.j have rank \(1\).

Complex multiplication

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

Modular form 139650.2.a.j

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} - 4 q^{11} - q^{12} - 2 q^{13} + q^{16} + 2 q^{17} - q^{18} + q^{19} + O(q^{20})\) Copy content 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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.