We argue that for all integers
N
≥
2
N \geq 2
and
g
≥
1
g \geq 1
there exist “multiradical” isogeny formulae, that can be iteratively applied to compute
(
N
k
,
…
,
N
k
)
(N^k, \ldots , N^k)
-isogenies between principally polarized
g
g
-dimensional abelian varieties, for any value of
k
≥
2
k \geq 2
. The formulae are complete: each iteration involves the extraction of
g
(
g
+
1
)
/
2
g(g+1)/2
different
N
N
th roots, whence the epithet multiradical, and by varying which roots are chosen one computes all
N
g
(
g
+
1
)
/
2
N^{g(g+1)/2}
extensions to an
(
N
k
,
…
,
N
k
)
(N^k, \ldots , N^k)
-isogeny of the incoming
(
N
k
−
1
,
…
,
N
k
−
1
)
(N^{k-1}, \ldots , N^{k-1})
-isogeny. Our group-theoretic argumentation is heuristic, but it is supported by concrete formulae for several prominent families. As our main application, we illustrate the use of multiradical isogenies by implementing a hash function from
(
3
,
3
)
(3,3)
-isogenies between Jacobians of superspecial genus-
2
2
curves, showing that it outperforms its
(
2
,
2
)
(2,2)
-counterpart by an asymptotic factor
≈
9
\approx 9
in terms of speed.