curve #6051

y² + y = x³ − 58073034746804470178931067x + 167129345773255617091343410197099837132

a-invariants: [0, 0, 1, -58073034746804470178931067, 167129345773255617091343410197099837132]
c-invariants: [2787505667846614568588691216, -144399754748092853166920706410294259282264]
rank (lower bound): ≥ 20
torsion subgroup: trivial
conductor (N): 5316123783320990439696445571594518583840498086117969860441212285045
discriminant (Δ): 467681421293787842456135685028114683373959831198185640841966834110026414453125
Faltings height: 13.6921
naive height: 189.5848
primes of bad reduction: 5, 7, 67, 7723, 30137, 23988253331557, 406038821038539175291540917466825078779923
regulator: 16199961162059004320.2162667746127137941418233914325349926087543962818257509610
submitted by: apkorte
submitted at: 2026-10-28 17:26:00 UTC
last updated: 2026-10-28 17:26:00 UTC

Witness: 20 independent points log in to add more points →

(-24527022258, 12982822868476681062)
(-656047229758, -14315922532206973563)
(14548322173367, -49004795931498154563)
(3710373662117, -1654366673927243938)
(6054561171767, -6121189265992303038)
(1738665316377, 8450780145894655502)
(2305815991412, -6744119435656890193)
(-3563068893633, 18133195279186826562)
(4936280925565, -863854489999368802)
(16277314191722, -59452050346794610243)
(4886798955342, 196947772845840537)
(-6231278099183, 16942412980560590862)
(3645697822882, -1966720558610051878)
(11966028440117, -34432420096790964063)
(3896592616717, -77744773428317538)
(4963287516792, 1078382458426373012)
(6084037345242, -6246165332449048563)
(15573363701313/4, 1732288738580285581/8)
(-863165692506468/121, -19669219758677956624728/1331)
(6357207626367, -7407277499645386563)

Commentary

Specialization at T = -9/23 of the rank-17 fibration of X1008 given in curve#3589. Found by Claude (Anthropic): a Mestre-Nagao sieve over the fibration, then a 2-covering point search seeded with its generic sections.

last edited by apkorte at 2026-10-28 17:26:00 UTC · history