curve #4123

y² = x³ + x² − 4736178915182050173885681745270990279486998075000968421983x + 125027163430012620524072208784162791864320845926058536811432184897446397320992204578538

a-invariants: [0, 1, 0, -4736178915182050173885681745270990279486998075000968421983, 125027163430012620524072208784162791864320845926058536811432184897446397320992204578538]
c-invariants: [227336587928738408346512723773007533415375907600046484255200, -108023469203530904132798388390880671698345641330193652147715452951885942730937543661388000]
rank (lower bound): ≥ 21
torsion subgroup: ℤ/2ℤ
conductor (N): 23006300323005732981493739280611137630592891352244258300189393439988018703931591002792570449685679400
discriminant (Δ): 46367134822119625641792032230943378907267783581599119945762845158641727667352379264764226761824120862686109221020055476131390747360316507763526105599787179162320254869250000
Faltings height: 31.9888
naive height: 410.0213
primes of bad reduction: 2, 3, 5, 7, 13, 23, 41, 53, 97, 257, 347, 353, 383, 419, 433, 563, 587, 701, 1429, 1889, 2053, 4099, 4241, 5557, 8221, 9901, 12619, 29863, 33347, 240677, 26559851, 48997456307
regulator: 382064325611339171758149033.08950347897454250440236122499957762229954325679407131
submitted by: wgxli
submitted at: 2026-10-09 21:23:34 UTC
last updated: 2026-10-09 21:23:34 UTC

Witness: 21 independent points log in to add more points →

(42167323854500131527924067623, 540539970409306300782415971517416668737275)
(43310002171472009234515598323, 1068762480373584694353661206122252859316425)
(44013371330742912338455681627, 1354122017849043262388051784613139502904047)
(-43352246239224753620122431938, 15775747158627518127236127080423215208932458)
(-70918157878979600802609631481, 10209481853751825272453345386038270529009509)
(169331926594768186414522934479, 64640128595736465404258723108682841658024019)
(578023827617047268201061263107, 436476616968125184400190238020691488697237543)
(3770390474794548241839122284939, 7319942065714634945534727971497484168678390079)
(375477666549421768320662828266/9, 6022251150448833035836412456200021636658372/27)
(15645631232147609795348732499454, 61885006398124951224120060762485927295731915994)
(336378844600065555369834942793/16, 377261543335849811497382643392150965867506675/64)
(478834668403896883392516835297/16, 203300253551291779019827574374730621165704647/64)
(399205456121643806553552898831/25, 914043770572617979328554396248651093736460721/125)
(-1511390945270535568364929871333/121, 17967866904591013051806391457744887364067351093/1331)
(-4341241006470853568369061544601/225, 48818194855406831925565471474838741918852263243/3375)
(25110522396090509349450222147523/289, 94435265654201532240427639712687842660324293609/4913)
(13208037850563726981779966228119/625, 91611073617110477638509923963018853707601904653/15625)
(169617486008033917117941791392147/4489, 38587034112953210496613642378059914452950501675/300763)
(154549026037185926839391937923839/3481, 309210276136709347749728321071465185558822164961/205379)
(7155658184289078327667827066254218/143641, 194126027132096297781860900286955695075650195732100/54439939)
(61661568891669229712160152442857482/994009, 8287851631488176662273422937821232459726274750636700/991026973)

Commentary

2-isogenous to curve #4122

last edited by wgxli at 2026-10-09 21:23:34 UTC · history