1 | | Computation of isogenies of prime degree p is expensive when the degree is neither a "genus zero" prime [2,3,5,7,13] or a "hyperelliptic prime" [11, 17, 19, 23, 29, 31, 41, 47, 59, 71] (for these there is special code written). In one situation we can save time, after factoring the degree ~~(p^2-1)/2~~ division polynomial, if there is exactly one factor of degree (p-1)/2, or one subset of factors whose product has that degree, then the factor of degree (p-1)/2 must be a kernel polynomial. Then we do not need to check consistency, which is very expensive. |

| 1 | Computation of isogenies of prime degree p is expensive when the degree is neither a "genus zero" prime [2,3,5,7,13] or a "hyperelliptic prime" [11, 17, 19, 23, 29, 31, 41, 47, 59, 71] (for these there is special code written). In one situation we can save time, after factoring the degree {{{(p^2-1)/2}}} division polynomial, if there is exactly one factor of degree (p-1)/2, or one subset of factors whose product has that degree, then the factor of degree (p-1)/2 must be a kernel polynomial. Then we do not need to check consistency, which is very expensive. |