Elliptic curves
We count the simple points on the curve
y
^{2}
=
x
^{3}
+
Ax
+
B
over the integers modulo
p
, for odd primes
p
between
and
, and determine the structure of the group. The coefficients are:
A
=
B
=
For
p
=
, we also show the addition table (if it is not too large), the number of elements of each order, the structure of the group, and a crude graph of the finite part of the curve (if it is not too large). The prime
p
need not be within the limits given above.