Hypergeometric Motives over $\Q$

Browse Hypergeometric Families

The table gives for each degree $d$ and weight $w$ shown, the number of corresponding hypergeometric families.

$w$ \ $d$	1	3	5	7	9	2	4	6	8	10
0	1	3	7	21	13	3	11	23	51	23
2		10	93	426	1836		30	234	1234	4475
4			47	414	2878			84	894	5737
6				142	1263				204	1936
8					363					426
1						10	74	287	1001	2197
3							47	487	3247	14397
5								142	1450	10260
7									363	3407
9										812

Families above are separated by type – those with odd weight and even degree are symplectic, otherwise they are orthogonal. Boxes are blank for combinations of weight and degree which cannot occur.

A random family of hypergeometric motives from the database.

A random hypergeometric motive from the database.

Find a specific HGM

Search by label

an HGM label encoding the triple $(A, B, t)$

Search for families of HGMs

Enter values into one or more boxes to restrict the list of families returned.

Degree	e.g. 4	Weight	e.g. 3
Family Hodge vector	e.g. [1,1,1,1]	$A$	e.g. [3,2,2]	$B$	e.g. [6,4]
Prime $p$		$A_p$	e.g. [2,2,1,1]	$B_p$	e.g. [2,2,1,1]
		$A^\perp_p$	e.g. [2,2,1,1]	$B^\perp_p$	e.g. [2,2,1,1]

Search for individual HGMs

Enter values into the boxes above and the boxes below to obtain the list of corresponding hypergeometric motives.

Conductor	e.g. a value, like 32, a list, like 32,64, or a range like 1..10000
Hodge vector	e.g. [1,1,1,1]
Specialization point $t$	e.g. 3/2 (1 has an associated degree drop and is always in the database)
Root number $\epsilon$	1 or -1, with -1 occurring only in the symplectic case
Results to display