Alf van der Poorten on Mon, 7 Sep 1998 14:25:30 +1000

 Pari Bug (elltors)

```My student Xuan Chong Tran has noticed the anomaly
---
? e=[0,0,0,-3601/768,-118151/55296];
? v=ellinit(e)
%2 = [0, 0, 0, -3601/768, -118151/55296, 0, -3601/384, -118151/13824,
-12967201/589824,
3601/16, 118151/64, 4625, 46694890801/18944000,
[2.3648131003232463559942610477173002322,
-0.47916666666666666666666666666666666666,
-1.8856464336565796893275943810506335655]~,
1.6806015939329474190939890379476241899,
1.9713908822102882979386345857169752777*I,
-0.96395806517810494401053543079449651620,
-3.0000749804811519786571547270840069242*I,
3.3131226589074899100884385162462589725]
? p=[-71/48,-5/4];
? ellorder(v,p)
%4 = 6
? elltors(v)
%5 = [2, [2], [[0, 0]]]
? ?elltors
elltors(e): torsion subgroup of elliptic curve e: order, structure, generators
---
where PARI reports both that a point \$p\$ on the elliptic curve \$e\$ has
order \$6\$, and that the torsion subgroup of \$e\$ has order \$2\$.

It might be interesting for users to check the extent of this strange case
of \$6\$ dividing \$2\$.
------------------------
Alf vdP, Macquarie University, Sydney
alf@mpce.mq.edu.au   phone: +61 2 9850 8947 fax: +61 2 9850 8114
home: +61 2 9416 6026   mobile: +61 4 1826 3129 (from MQ: #6335)
```