curve #2942

y² + xy = x³ − 103747596714222999582133183601126173090660x + 13718942305952740368641219874353441801908454337456892365155600

a-invariants: [1, 0, 0, -103747596714222999582133183601126173090660, 13718942305952740368641219874353441801908454337456892365155600]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/6ℤ
conductor (N): 1375141440105163911081601881101260056990
discriminant (Δ): -9838043049096501137873029601269735247320109492134608494393362667226572721436819368338083293939323960488245232761358007808000
Faltings height: 22.5388
naive height: 295.0709
primes of bad reduction: 2, 3, 5, 7, 13, 17, 23, 29, 31, 37, 47, 149, 167, 479, 617, 971, 1907, 6961, 8693281
regulator: 1720782250.72519802643238750040741716831593094339942573
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:29:24 UTC
last updated: 2026-09-26 20:29:24 UTC

Witness: 8 independent points log in to add more points →

(285898651814442710487790/1681, 68698340814513357553246877515994090/68921)
(125651799867903472880, 1633005743562188872273976648540)
(534479031744001153880, 10533351570788889740799869048540)
(1793463313477957283543090/6889, 1193112916119856748446548010943681650/571787)
(605802921015861448079150/24649, 12941864429035178235877747568015633330/3869893)
(420840751832344849543246205424106756/2751655121600841, -172554003246127863444385971012923312543620342065945988/144341429174475589281861)
(154824810006709362065264977211000/2604314936521, -11708685421456822007543023014921406441318012129460/4202814797093288069)
(61322632269881729727223640/100489, 424591947367851956903165194659395837500/31855013)

Commentary

2-isogenous image of D-z6old678-081, rational kernel x=187326769206971886920. Source: https://dujella.github.io/tors/z6old678.html. Independent witness points transported by the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independence is certified.

last edited by Natanael Wildner Fraga at 2026-09-26 20:29:24 UTC · history