Why is my SP_HELPINDEX showing a lot of indexes?
The indexes you are seeing are hypothetical indexes created by Database Engine Tuning Advisor.

DTA leaves a bit of a mess behind if it crashes or if you kill it because it runs too long.

They all include _dta_ in the name and you can see the hypothetical in the description.

Try the query from Brent as you will most likely have some of these on other tables too.

WITH hi AS (
SELECT QUOTENAME(SCHEMA_NAME(o.[schema_id])) +'.'+ QUOTENAME(OBJECT_NAME(i.[object_id])) AS [Table] , QUOTENAME([i].[name]) AS [Index_or_Statistics], 1 AS [Type]
FROM sys.[indexes] AS [i]
JOIN sys.[objects] AS [o]
ON i.[object_id] = o.[object_id]
WHERE 1=1 
AND INDEXPROPERTY(i.[object_id], i.[index_id], 'IsHypothetical') = 1
AND OBJECTPROPERTY([o].[object_id], 'IsUserTable') = 1

UNION ALL

SELECT QUOTENAME(SCHEMA_NAME(o.[schema_id])) +'.'+ QUOTENAME(OBJECT_NAME(o.[object_id])) AS [Table], QUOTENAME([s].[name]) AS [Index_or_Statistics], 2 AS [Type]
FROM sys.[stats] AS [s]
JOIN sys.[objects] AS [o]
ON [o].[object_id] = [s].[object_id]
WHERE [s].[user_created] = 0
AND [o].[name] LIKE '[_]dta[_]%'
AND OBJECTPROPERTY([o].[object_id], 'IsUserTable') = 1
)
SELECT [hi].[Table] ,
       [hi].[Index_or_Statistics] ,
       CASE [hi].[Type] 
       WHEN 1 THEN 'DROP INDEX ' + [hi].[Index_or_Statistics] + ' ON ' + [hi].[Table] + ';'
       WHEN 2 THEN 'DROP STATISTICS ' + hi.[Table] + '.' + hi.[Index_or_Statistics] + ';'
       ELSE 'DEAR GOD WHAT HAVE YOU DONE?'
       END AS [T-SQL Drop Command]
FROM [hi]


You should delete those, they aren't used anyway

EDIT:
Not sure why but the OP had issues with the query from Brent and this select worked on his environment

SELECT t2.NAME AS table_name
    ,t1.NAME AS index_name
FROM sys.indexes t1
INNER JOIN sys.tables t2 ON t2.object_id = t1.object_id
WHERE t2.NAME = 'MyTable'
    AND t1.NAME LIKE '%_dta_%'
    AND t1.is_hypothetical = 1