find_totally_split.py

from sage.all import *

def is_good(N):
    number_of_opt_curves = 0
    for d in divisors(N):
        number_of_opt_curves += number_of_divisors(N//d) * len(list(cremona_optimal_curves(d)))
    dim = dimension_cusp_forms(N)
    return number_of_opt_curves == dim

good_primes = [2, 3, 5, 7, 11, 13, 17, 19, 37]

to_be_checked = {1}
good = set()
while to_be_checked:
    new_goods = set()
    for x in to_be_checked:
        # add the children to to_be_checked if good
        if is_good(x):
            good.add(x)
            new_goods = new_goods.union({x*p for p in good_primes})
    # now check the new_goods
    to_be_checked = new_goods
list_of_goods = list(sorted(good))
print('There are {} good integers and they are:'.format(len(list_of_goods)))
print(list_of_goods)