curve #4592

y² + xy + y = x³ − 2813035593801150909512534x + 1813939483996375619018752861172039532

a-invariants: [1, 0, 1, -2813035593801150909512534, 1813939483996375619018752861172039532]
c-invariants: [135025708502455243656601609, -1567243714173071073394956154918127058277]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/3ℤ
conductor (N): 228807620212586562666564901674588770
discriminant (Δ): 3199085908104098429442921705210829177457785712821495290514784216766901100
Faltings height: 12.8196
naive height: 180.5025
primes of bad reduction: 2, 5, 7, 11, 13, 19, 23, 37, 41, 97, 443, 1979, 2239, 181089821480563
regulator: 1076385297768.110838392372628937943472859482195587382950393
submitted by: Maksym Voznyy
submitted at: 2026-10-18 15:20:44 UTC
last updated: 2026-10-18 15:20:44 UTC

Witness: 10 independent points log in to add more points →

(4973823189938838926226/4903500625, -22266633471846518756928979939976/343367631265625)
(2787785780499459/484, 141543491604973942880777/10648)
(449762956782322957323479511/85344912009361, 9104572264110081867169195412295929579159/788436011817151080391)
(3073547841476406285354573099/2970197353233289, -17042191300703447205039688805106764024123/161874321145892638821413)
(379465977588359/289, -3044748820842022792073/4913)
(4540566996473558982634236/3213977661049, 4679189947893590185997262779831978515/5761880949689222093)
(219502493834821/81, 2736551122577168598991/729)
(7954151321166269/7225, 139170772233920545180883/614125)
(725673451010356/729, -209347357934073617540/19683)
(544359508553965140126559806/546480809471041, 190888374954904712161492207930862796081/12775043082867053013089)

Commentary

t = 4/447 for y^2 + (7t^2+309) x y - 91 (t^2-1)(t^2-25)(t^2-121) y = x^3 from https://github.com/Layr-Labs/elliptic-rank-challenge-public/blob/main/submission/board/3-r12-z3k3.ec

last edited by Maksym Voznyy at 2026-10-18 15:20:44 UTC · history