curve #102

y² + xy + y = x³ − x² − 354423968717233792815730830x + 2561986646153119712343318111147387184797

a-invariants: [1, -1, 1, -354423968717233792815730830, 2561986646153119712343318111147387184797]
rank (lower bound): ≥ 18
conductor (N): 2300421877446970281453428041661531850670855338680544890937950
naive height: 195.0112
Faltings height: 14.0578
discriminant (Δ): 13821441904429578871006127124264988888315125425652332382713954798587645696000000
primes of bad reduction: 2, 5, 11, 19, 29, 31, 67, 97, 1194256489, 31549128016279775676380684297728489659559
regulator: 28029078662856042.835630945014296244921316895372976514932855516252265257542
submitted by: Alexey Pozdnyakov
last updated: 2026-07-01 22:32:42

Witness: 18 independent points

(18767601803769, -50206358006201696685)
(10063361108249, 3797268895762353875)
(14463240795049, -21479423046961879325)
(11845650903449, 5077316719636289875)
(10180034695969, -2987808036154910885)
(27862066360089, 119650218507818587155)
(11579125906089, -3248326623828937245)
(101778703261921/9, -10313188444042479295/27)
(11565547025193, 3147828265004909171)
(11951310161719, 5762553083670604165)
(12606449162989, 9869546987446928155)
(2192939908113, -42371005295704069429)
(5454584277089, -28125412966729382245)
(29333052772769, 131926590527912797315)
(471775179472089, -10239102436034213707245)
(75605547614289, 638703266730899417355)
(-192585037525199/9, 503686169623613931185/27)
(562483151941701/49, 848706767424556824125/343)

Commentary

Generated with assistance from OpenAI Codex, based on GPT-5, during a local generalized Mestre/Fermigier quartic-family search. I searched nondegenerate Mestre (u,v) families in the box [-3,3]^2, focusing here on denominator bands 41<=n<=60 and 61<=n<=80 for specializations T=m/n. For each family I used a Mestre-Nagao sieve at prime bound M=200, rescored per-family survivors at M=1000, computed exact minimal-model heights for the global top rows, and certified the top unique models by height and score using GP famcert. This rank >= 18 conductor candidate came from family mestre_u3_vm1 at T=101/62 in the n=61..80 band; famcert certified 18 independent points, and Sage computed log conductor 138.988198, below the current ICARM rank >= 18 conductor frontier if accepted.

last edited by Alexey Pozdnyakov at 2026-06-23 23:58:10 · history