curve #4604

y² + xy = x³ − 19063790245695582731480095x + 32020715664069264952386769113058040025

a-invariants: [1, 0, 0, -19063790245695582731480095, 32020715664069264952386769113058040025]
c-invariants: [915061931793387971111044561, -27665898333757217511759858595638813148441]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/3ℤ
conductor (N): 1176541376429733882533000620110890
discriminant (Δ): 471358479271697853963600730303399961710479562011918423699731000000000000000
Faltings height: 13.2711
naive height: 186.2431
primes of bad reduction: 2, 5, 7, 13, 19, 37, 67, 79, 97, 433, 457, 661, 1559, 4339, 7321
regulator: 1053146660864.171020281398895784677263328353963317945387372
submitted by: Maksym Voznyy
submitted at: 2026-10-18 23:17:01 UTC
last updated: 2026-10-18 23:17:01 UTC

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

(2942557545672384191115190585590/21160560517956601, 5045170358890773081019422752797251104000366295/3078156887536876972730099)
(981348855047847770/344569, 184015364780745838633686195/202262003)
(3599515975205160866710/1161650889, 65063362157818887697554370916735/39592547249787)
(172116887306660969590/7284601, -2221956291985248352941398673705/19661138099)
(54317919490518440/121, -12658849437663529990356945/1331)
(1005168660600100222334127590/111370051346401, 28673020349859581791133463676932687122205/1175310537238890379601)
(26282213221886219861215/8728417476, -1129530395941547213410477977561295/815461131112776)
(174339113943915112520542990/67425135660961, -67878300845958775474640529820211672595/553646735375271501041)
(767411257204962086189750/288176786041, -57606441158653807090306085632772055/154699350459315661)
(2950140279090, -1206607333923420795)

Commentary

t = 115/273 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 23:17:01 UTC · history