The number on Negi's Pactio card is 496.

496 is a perfect number.

"In mathematics, a perfect number is defined as a positive integer which is the sum of its proper positive divisors, that is, the sum of the positive divisors excluding the number itself. Equivalently, a perfect number is a number that is half the sum of all of its positive divisors (including itself), or σ(n) = 2n."

"496 is most notable for being a perfect number, and one of the earliest numbers to be recognized as such. As a perfect number, it is tied to the Mersenne prime 31, 25 - 1, with 24 ( 25 - 1 ) yielding 496. Also related to its being a perfect number, 496 is a harmonic divisor number, since the number of proper divisors of 496 divided by the sum of the reciprocals of its divisors, 1, 2, 4, 8, 16, 31, 62, 124, 248 and 496, (the harmonic mean), yields an integer, 5 in this case."

1+2+3+.....+30+31 = 496

There are 31 students in his class.

This, in my mind, just triggered two main thoughts:

1) Seeing as Negi's Pactio picture doesn't show us any Artifact that he doesn't already have, perhaps it doesn't function that simply. I theorize that his Pactio is actually a special item that allows him to use the Artifact powers of all his Partners. Some of those powers (especially Konoka's) would come in handy for this fight.

2) The 1-31 adding up to his Pactio number tells me that Ken is foreshadowing for the Harem ending. IOW, we won't get a proper pairing at the end, but rather a

typical Harem ending. I hope this isn't the case, but now the thought it locked in my mind.