There is a [paper](https://doi.org/10.1023/A%3A1022669121502) by Rizzo in which tables are given that specify the local root numbers of an elliptic curve based on $(a, b, c)$ where $(a, b,c)$ are non negative and minimal so that $a\equiv c\_4\pmod{4}$, $b\equiv c\_6\pmod{6}, c\equiv\Delta\pmod{12}$ where $c\_4, c\_6, \Delta$ are standard invariants. Rizzo then has tables that give the value of the root number based on this (and a little bit more). However, given this, there are certain things about the tables that do not make sense. For example, in Table I (corresponding to $p > 3$), there is a row in which the values of $(a, b, c)$ are $(\ge 4, 5, 10)$, which does not seem possible given the definition of $(a, b, c)$. I assume this is not an error with the table since this issue arises many more times in the tables corresponding to $p = 2, 3$. What is the definition of the triple $(a, b, c)$ if this is so?



Statement of a result by Rizzo
It’s been a long while, but the definition of (a,b,c) should be the minimal non negative triplet of integers such that (a,b,c) + k(4,6,12) = (c4,c6,Delta).


