curve #4060

y² + xy = x³ + 893214139646765693467090651189747907677183567006182755x + 330204019258291043572172000570021624274222060257836621923129047126519645260857137

a-invariants: [1, 0, 0, 893214139646765693467090651189747907677183567006182755, 330204019258291043572172000570021624274222060257836621923129047126519645260857137]
c-invariants: [-42874278703044753286420351257107899568504811216296772239, -285296272639163461646356608428187265318360730133140314455921647364555756680935408009]
rank (lower bound): ≥ 20
torsion subgroup: ℤ/2ℤ
conductor (N): 10440871783541742304283973928724932391253078912604073640431645403950958428574441994981529610
discriminant (Δ): -92711588029166326140974941948317084641306874554211735281761887814419532048610961519598062522914869868986076478928203285408037884650561910357990904165682286934944000
Faltings height: 30.1486
naive height: 384.3258
primes of bad reduction: 2, 3, 5, 11, 31, 37, 47, 67, 71, 79, 83, 137, 269, 271, 461, 659, 797, 1069, 1447, 2389, 2861, 4049, 5851, 14629, 27749, 45503, 522881, 325634333, 12647136419
regulator: 4266384506762103589697481.65296783666088102155520487975368956875804939205106597
submitted by: wgxli
submitted at: 2026-10-08 21:09:26 UTC
last updated: 2026-10-08 21:09:26 UTC

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

(16037457867864523537879354, 18561600906842601757103788903186966814983)
(-274585308441820058745359872, 8014836589904338388672028465363350898041)
(-287861705530003103808438466, 7016295118077097596859023205403354141003)
(-321371790374177158276963366, 3155783403785619429707746582001849768063)
(333192233369063377014083534, 25783833247715887674552855491135468724503)
(415749345022793919475802342, 27810401923233824541378804131154372626003)
(996140445791680864733693474, 46994007265522458338431177218375500519423)
(1137243569770114713283972394, 53073809451742910314246864172149469219423)
(1414304045185688564763466874, 66501507099728610923712349505009180445503)
(4540455077362909052590453754, 313034517478890904979002545713244422988863)
(6785564359325574537214837994, 564645820030081275692722474523316811917023)
(9665773361230310320415519594, 954991992428674438255842240287071543394783)
(29080319778286205097999219269/16, 5709142856996493573917811575639102029710407/64)
(32588264957962888266746020406/49, 11972709532110754413483202886635277719154369/343)
(69449644767455644537374672304/81, 30289574789072739257838188752026097932747727/729)
(-94359043516519207460071460074/289, 9528797039854354149701752210464273381446419/4913)
(-213967841327006633559772059733/676, 69803022587273606715737658337828110501018703/17576)
(97022505662227020824237351137514/48841, 1076339455284497099241952777394629164675386295163/10793861)
(11988323229620062675499075295583418/2430481, 1338266398104082994700204781866380158279385431477969/3789119879)
(-8366264765142470393942609682619054/47706649, 4273078696880799462431933401197384766130191719408509/329509824643)

Commentary

2-isogenous to curve #4059

last edited by wgxli at 2026-10-08 21:09:26 UTC · history