curve #314

y² = x³ + x² − 5259979010001805005968016x + 4642551389959286676185695447422235620

a-invariants: [0, 1, 0, -5259979010001805005968016, 4642551389959286676185695447422235620]
c-invariants: [252478992480086640286464784, -4011164400926338562179321386414530364352]
rank (lower bound): ≥ 18
torsion subgroup: trivial
conductor (N): 145855597016413173717093065412472683801352457871296529840
discriminant (Δ): 2890929371722789110949306313392128089803170966886362237901259169725260800
Faltings height: 12.9079
naive height: 182.3801
primes of bad reduction: 2, 3, 5, 7, 13, 59, 2069, 23831, 176592536225594123223340949652953524751227
regulator: 1654927905997430702.5093919430042470480632172338368733749155977929860404374
submitted by: C. R. Hill
submitted at: 2026-08-24 01:58:08 UTC
last updated: 2026-08-24 01:58:08 UTC

(-16482328548576198/6241, 166379936565244843857780/493039)
(-5659979172803466/2209, -118314679144771907074368/103823)
(1002460149787152, -31739460502428886506390)
(-168478746384816/121, -4051796527631485983714/1331)
(176401596607977/16, 2295792302138269065405/64)
(1307309331072, 19970243846526870)
(5784286914353409658/4297329, -307657994676127822433814380/8908363017)
(33062664429861486/24649, -83048351311764662106192/3869893)
(1282304475825052911/982081, 24282311042834950983886554/973242271)
(836450562392319/625, 141404588723156471622/15625)
(1440824533313913552/1100401, -13784437241185352260583610/1154320649)
(1275537803232, 92439705229956630)
(2712748775247, 3215071393107043470)
(1264895703582, -114063632905141920)
(2781129678474, -3394852297697850444)
(315746253262272/361, -5783762931973896222990/6859)
(1377682472664, -104039547001445094)
(-2010826486553238/841, 45953449007909090473020/24389)

Found with Rank Hunter v0.7.17; rigorous rank lower bound >= 18.

last edited by C. R. Hill at 2026-08-24 01:58:08 UTC · history