curve #376

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y² + xy = x³ − 1445990013167463346228809073545620x + 21128721995181552195912389455017474056877615305616

a-invariants: [1, 0, 0, -1445990013167463346228809073545620, 21128721995181552195912389455017474056877615305616]
rank (lower bound): ≥ 22
torsion subgroup: trivial
conductor (N): 176634054787705380330890095321066714644533156566592717278673628271112803086 ★ record for rank ≥ 22
naive height: 240.6759
Faltings height: 17.8487
discriminant (Δ): 643031218468664206983673895482549260328406935268474125048298063324864932907314896916917745512087552 ★ record for rank ≥ 22
primes of bad reduction: 2, 3, 7, 13, 37, 107, 179, 449, 535727176489, 737847126898976814871, 2572094103432626869737285466901
regulator: 1286866514404761900277.157009902989173932432515611549332238957901532546779504462846
submitted by: wgxli
submitted at: 2026-08-26 13:40:43 UTC
last updated: 2026-08-26 13:40:43 UTC

Witness: 22 independent points

(-300067237192867438747561129106315521016/7001135912730013470025, -1224842846959625355656500141103833452887764022443856693212/585804580273174357885733289618875)
(65308906035445333480, -527786819244869489080073951444)
(12237777679025389576/25, -42685349953525736742075882916/125)
(66306354064991464/9, -89040507691388997337430108/27)
(542075574390339625512/5041, 11919509562617917909032449999604/357911)
(736842914523687573682312/41229241, 264007525997474856903930330268465084/264732956461)
(362666083518189238804516700440/15951181295449, -4731463491387778962971319814056493692530932/63707311317624692957)
(705854049802192324/81, 2209934439324809124544959200/729)
(3887805802863319378164706/85692049, 5547832710869757693099442276431001718/793251297593)
(-31668383366411976859060496/2759295841, -872221957806339683569573560786485666836/144943051231889)
(18190256750263474024/25, -77477622140228880712582370692/125)
(-1043788945175740061477520704/72672837241, -122243140471600187123237457061427423256196/19591070790591539)
(199130268109237160104/9409, -67561633800821545851430853972/912673)
(54811163143310998415662504/2583180625, 1164134151422669476852137438013052108/131290155265625)
(166665683341618134, -66405417744127049211932190)
(1128260110994284276/49, -69978420083410609922501552/343)
(54374737692369295336/1681, -197363256956621295806026958644/68921)
(126707348658998268989504776/234304249, -1422838184676389757788959714030243258652/3586495139443)
(5856763782648859579336069684077004/20040461510249569, 444596060628158791604146927164202667578933609710424/2837014646872498940020753)
(217281200083373531051451304/3388520521, 2733612576758332146203791050411318644516/197249168047931)
(27121942191436313010551898417640/62820635846809, -140717307559761924466484580843097784776181866748/497913030228108253123)
(3466862700868472579644568119260/1392912167089, -6454380567047583465150790936289935961113593912/1643938619105278313)

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