History of $x$-coordinates of the torsion points of elliptic curves over $\mathbb{Q}$

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2026-09-20 01:29 zeta3 keep T346 definition focused current
2026-09-20 01:28 zeta3 repair T346 critique findings
2026-09-20 01:16 bmatschke interactive a real root is written as a real number, not as a + i * [0, 0] reviewed
2026-09-20 01:05 zeta3 shorten definition
2026-09-20 01:04 zeta3 record measured range and exact roots
2026-09-20 01:03 zeta3 with Codex CLI, filled torsion x-coordinate roots
2026-09-20 00:56 zeta3 with Codex CLI, filled torsion x-coordinate roots
2026-09-20 00:48 zeta3 drafted torsion-coordinate table

What changed between 2026-09-20 01:28 and 2026-09-20 01:29

from line 1 (7 lines, 1 fewer than before) @@ -1,8 +1,7 @@
 Title: $x$-coordinates of the torsion points of elliptic curves over $\mathbb{Q}$-Definition: 'Let $E/\mathbb{Q}$ be the elliptic curve whose reduced global minimal-  Weierstrass model is recovered from $(c_4,c_6)$ using the convention of HREF{Division_polynomials_psi_n_of_elliptic_curves_over_mathbb_Q}[the-  division-polynomial table]. The entry is the $x$-coordinate $x(P)$ of a point $P\in-  E[n]\setminus\{O\}$: the root numbered $k$ of the division polynomial $F_{E,n}(x)$,-  whose roots are exactly those $x$-coordinates.'+Definition: 'Let $E/\mathbb{Q}$ be the elliptic curve with reduced global minimal+  Weierstrass model recovered from $(c_4,c_6)$. The entry is the $x$-coordinate $x(P)$+  of a point $P\in E[n]\setminus\{O\}$: the root numbered $k$ of the division polynomial+  $F_{E,n}(x)$, whose roots are exactly those $x$-coordinates.' Parameters:   N:
from line 30 (7 lines, 1 more than before) @@ -31,6 +30,7 @@
 Comments:   comment-model: The reduced global minimal model is the one used by Sage's Cremona-    database CITE{SageCremona}, and matches the curve convention in HREF{Division_polynomials_psi_n_of_elliptic_curves_over_mathbb_Q}[the-    division-polynomial table]. Entry comments give Cremona labels.+    database CITE{SageCremona}. The recovery from $(c_4,c_6)$ uses the curve convention+    in HREF{Division_polynomials_psi_n_of_elliptic_curves_over_mathbb_Q}[the division-polynomial+    table]. Entry comments give Cremona labels.   comment-root-order: For fixed $(N,c_4,c_6,n)$, roots are ordered by increasing real     part and then by increasing imaginary part. 

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