Properties

Label 221760.js
Number of curves $6$
Conductor $221760$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("js1")
 
E.isogeny_class()
 

Elliptic curves in class 221760.js

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
221760.js1 221760jl5 \([0, 0, 0, -7632012, 8114950384]\) \(257260669489908001/14267882475\) \(2726634802190745600\) \([2]\) \(8388608\) \(2.6029\)  
221760.js2 221760jl3 \([0, 0, 0, -504012, 111631984]\) \(74093292126001/14707625625\) \(2810671026831360000\) \([2, 2]\) \(4194304\) \(2.2563\)  
221760.js3 221760jl2 \([0, 0, 0, -155532, -22044944]\) \(2177286259681/161417025\) \(30847273854566400\) \([2, 2]\) \(2097152\) \(1.9097\)  
221760.js4 221760jl1 \([0, 0, 0, -152652, -22956176]\) \(2058561081361/12705\) \(2427963310080\) \([2]\) \(1048576\) \(1.5632\) \(\Gamma_0(N)\)-optimal
221760.js5 221760jl4 \([0, 0, 0, 146868, -97403024]\) \(1833318007919/22507682505\) \(-4301285109568634880\) \([2]\) \(4194304\) \(2.2563\)  
221760.js6 221760jl6 \([0, 0, 0, 1048308, 663636976]\) \(666688497209279/1381398046875\) \(-263989277798400000000\) \([2]\) \(8388608\) \(2.6029\)  

Rank

sage: E.rank()
 

The elliptic curves in class 221760.js have rank \(0\).

Complex multiplication

The elliptic curves in class 221760.js do not have complex multiplication.

Modular form 221760.2.a.js

sage: E.q_eigenform(10)
 
\(q + q^{5} - q^{7} + q^{11} + 2 q^{13} + 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.