# Revision history [back]

Here is a piece of code trying to compute the rank of all elliptic curves $E(a,b)$ of the shape $y^2=x^3+ax+b$ for $a,b\in[2010, 2021]$. Sometimes, there it will be "harder" to compute the rank, so the code will not deliver a computed rank. We fill in a dictionary with keys $(a,b)$ and values the corresponding rank for the key, when it could be computed, else the value is showing a None.

R, dic = [2010..2021], {}
for a, b in cartesian_product([R, R]):
try:
E = EllipticCurve(QQ, [a, b])
E.two_descent(second_limit=13, verbose=False)
r = E.rank(only_use_mwrank=False)
dic[(a, b)] = r
print(f'({a}, {b}) -> {r}')
except Exception:
dic[(a, b)] = None


To see which cases could not be computed...

[key for key, val in dic.items() if val == None]


and there is no None value. But well, in other cases we may have the situations. (Also maybe consider first commenting that two_descent line, it may be time consuming, but it may find more curve ranks.)

 2 No.2 Revision slelievre 16674 ●19 ●147 ●330 http://carva.org/samue...

Here is a piece of code trying to compute the rank of all elliptic curves $E(a,b)$ of the shape $y^2=x^3+ax+b$ for $a,b\in[2010, 2021]$. Sometimes, there it will be "harder" to compute the rank, so the code will not deliver a computed rank. We fill in a dictionary with keys $(a,b)$ and values the corresponding rank for the key, key when it could be computed, else the value is showing a and None. otherwise.

R, dic = [2010..2021], [2010 .. 2021], {}
for a, b in cartesian_product([R, R]):
try:
E = EllipticCurve(QQ, [a, b])
E.two_descent(second_limit=13, verbose=False)
r = E.rank(only_use_mwrank=False)
dic[(a, b)] = r
print(f'({a}, {b}) -> {r}')
except Exception:
dic[(a, b)] = None


To see which cases could not be computed...

[key for key, val in dic.items() if val == is None]


... and get an empty list, so in this case there is was no None value. But well, in other cases we may have the situations. situation. (Also maybe consider first commenting that out the two_descent line, as it may be time consuming, consuming; but it may find allow finding more curve ranks.) ranks.)