History of Modular polynomials for the $j$-invariant

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when	who	what
2026-09-02 01:29	bmatschke	record that all twelve entries were verified against the defining property, after phi_1 turned out to be wrong	current reviewed
2026-09-01 20:55	bmatschke	Phi_1 = x - y, not x + y. This table defines phi_n as vanishing on (j(n tau), j(tau)); for n = 1 that is the diagonal, and x + y vanishes there only at j = 0.
2026-08-14 21:32	bmatschke	how well the digits are known: exact (type Z[])
2026-08-13 22:08	bmatschke	how well the digits are known: exact (type Z[])
2026-08-09 09:16	flattening	entries rewritten as records with named parameters
2026-08-09 08:35	data-repository import	the current state of the data repository
2021-08-30 02:28	bmatschke	from the data repository, 1832084c
2021-08-30 02:03	bmatschke	from the data repository, da9f65d5
2021-08-29 22:22	bmatschke	from the data repository, 4d3062e0
2021-08-29 21:58	bmatschke	from the data repository, ea493078

What changed between 2026-09-01 20:55 and 2026-09-02 01:29

from line 10 (10 lines, 6 more than before) @@ -10,4 +10,10 @@

 Comments:   comment-more-data: More complete data is available at CITE{Suth}.+  comment-checked: 'Every entry has been checked three ways: its degree in $x$ is+    $\psi(n)=n\prod_{p\mid n}(1+1/p)$, it is symmetric in $x$ and $y$ for $n>1$ and+    antisymmetric for $n=1$, and it vanishes at $(j(n\tau),j(\tau))$ evaluated at+    2400 bits for three values of $\tau$. All twelve pass. The check was made after+    $\phi_1$ was found to read $x+y$, which vanishes on the diagonal only at $j=0$;+    it is $x-y$, and it was the only entry that was wrong.' Formulas: {} Programs: {}