curve #422

← home · all curves · JSON ↓

y² + xy + y = x³ − x² − 7563743114616965332438173567x + 250105033771561875331934803308050741991591

a-invariants

[1, -1, 1, -7563743114616965332438173567, 250105033771561875331934803308050741991591]

c-invariants

[363059669501614335957032331201, -216090749178627826518278912793644034435244449]

rank (lower bound)

≥ 19

torsion subgroup

trivial

conductor (N)

175007345314054296785277335340697651878439593395212342172414230

discriminant (Δ)

671601139256879286644864763242401235112684590481934864859859285100484452003840000000

Faltings height

14.8900

naive height

204.1931

primes of bad reduction

2, 5, 7, 11, 13, 17, 53, 79, 353, 383, 34290911, 125705707, 493512871, 122001816266124865447327

regulator

134550419705262164.8353748439626499808864762993943233742433550909076518759935

submitted by

Bhavik Mehta

submitted at

2026-08-29 17:02:02 UTC

later contributions

rank ≥ 18 → ≥ 19 · Jason Ma · 2026-09-03 16:32:02 UTC

Witness: 19 independent points log in to add more points →

(-98701531636279, -187372569287904714236)
(-38550758616809, -695988799050133979066)
(1338358266388971, 48861008805998774677014)
(-12117008407518901/169, -1430307938552210383640242/2197)
(37943122950931, 133187728339069300374)
(-1047084357869, 507960395500896423574)
(63062062748421, -154617301706338388286)
(-100120643103031, 61385694952052965636)
(26881695718921871, -4407402590186891281294586)
(490112248184841, 10689849743677205190084)
(345862121276961, -6245504928998079559246)
(139210573089181, 1376588092336909158624)
(1397170450270751, -52125600151015979217446)
(43651151694215, -55792907077527889358)
(-55133580099309, 706775157750374350934)
(44283323439091, -44693558817540930666)
(60148533734571, -112982837179616785386)
(377325764989891/1521, 29554238800133636483281466/59319)
(-38265598881509/81, -367171582419861242477914/729)

Commentary

From Elkies's rank-17 K3 fibration (arXiv:2608.25406), specialized at t = -29/13. The single point beyond the seventeen generic sections came from searching the 1311 norm-4 quartic covers.

last edited by Bhavik Mehta at 2026-08-29 17:02:02 UTC · history