curve #4008

y² + xy = x³ − 11329808084756532941745744081975x + 95053227636999993898925564809485431193456615081

a-invariants: [1, 0, 0, -11329808084756532941745744081975, 95053227636999993898925564809485431193456615081]
c-invariants: [543830788068313581203795715934801, -82125988678367995544417870097865784356840089332185]
rank (lower bound): ≥ 15
torsion subgroup: ℤ/2ℤ
conductor (N): 44025871847742350339136611296547024333859559593162
discriminant (Δ): -3810092021633327326305165313748236692206328424470137450671486982205553508062133107232244783787008
Faltings height: 17.2129
naive height: 229.8647
primes of bad reduction: 2, 3, 7, 11, 19, 53, 59, 137, 317, 379, 419, 647, 821, 1747, 2143, 2297, 4513, 5647, 10453, 191119
regulator: 14992366452696241234122.867365043604287738759853636397568705369499333
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:44:44 UTC
last updated: 2026-10-05 04:44:44 UTC

Witness: 15 independent points log in to add more points →

(97430992988026546329217/451584, 30408492470347160499607230276799729/303464448)
(173889451938532594820623746/112614607561, 10771543756066616272431226101528459430341/37791322619927941)
(3288818821442567019684/13225, 188591224304622888353462191288647/1520875)
(-1498201495698169590857173722/1061891091361, 359992381093546043615961358785475708168629/1094258593716774641)
(-33486094291674996352105428/6404320729, 54593063189836057727447092948499123757/512518574979683)
(-77905312488302483444430305037/18789502718596, 21664039177865846385201488678077651081722429/81446594381260020856)
(-10834933800367794548321527098/5648023174249, 4446350131124903367238631126251422478587417/13422849010923680693)
(3565130401807069326/961, 9610950145695430838963000883/29791)
(104573940393282840348464814/69151643089, 5187494025359068434261366326749627290843/18184600128185063)
(415727235900344322561838/384120801, 2182697563566038100286812016908533227/7528383578799)
(35595634575824761471116/32478601, 53630618644969136733938507646625479/185095547099)
(-1264917665674414217092242/544242241, 4188558446092161222192467414289181797/12696627240289)
(1496804195555085562653288462/283821409, 57909177867004055567673998334655216755819/4781539277423)
(10192137436108865471649261/3028961296, 51388742016483576286686129412611036351/166701913886656)
(583438125846676892150052517759782/34722611625241849, 13950338224480677165819615145695752910456832234671/6470212943319866028059507)

Commentary

Unlisted rational-isogeny neighbor of curve#3646 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 15: 15 independent points certified by the unchanged ICARM verifier, with a matching unconditional upper bound computed using PARI/GP 2.17.2 ellrank. This is an additional representative of a known isogeny class, not a claim of a new world rank record.

last edited by Odbayar Shinebayar at 2026-10-05 04:44:44 UTC · history