curve #1999

y² + xy = x³ − 1607547610816153924771616239522458946620595x + 763774825601709618476211526215291080160316198307742323284685537

a-invariants: [1, 0, 0, -1607547610816153924771616239522458946620595, 763774825601709618476211526215291080160316198307742323284685537]
rank (lower bound): ≥ 17
torsion subgroup: ℤ/2ℤ
conductor (N): 144709965057296981296158253023483904833485520354172293743617612639487430
discriminant (Δ): 13863272088520265276366564277613291735302839878801079136573662654079363767576597356457219249609948411465132567349733228512000000
Faltings height: 23.1726
naive height: 303.1635
primes of bad reduction: 2, 3, 5, 7, 11, 17, 67, 73, 103, 167, 211, 227, 283, 401, 641, 1249, 2111, 2927, 21149, 141689, 206279, 1251697, 4221313, 29338571
regulator: 80977028456173233801666329545.9912399238415537216551897512206615615765552
submitted by: Steps Unbounded
submitted at: 2026-09-26 04:55:21 UTC
last updated: 2026-09-26 04:55:21 UTC

Witness: 17 independent points log in to add more points →

(89778557876929549069288729324/58967041, 19452621130781701556914267836595087412965877/452807907839)
(397980870562835099302468719868365884/133635195284761, -231156119690229115391232505687873077711206439874994353/1544832078320311808509)
(48686387465129232014952632956334/47789894881, 141486928659466823224232585085687964274899204297/10447301130040529)
(1053794845495659424306637448823534040486/196735655965438489, -33323724627279395008375476819780776524182856726199373173539/87261890286525326673082237)
(324824533890987677409160357782242010871726/378057198917082283369, 30173316457758708925270997984717389018343983884500349155317789/7350828126171796733497886201653)
(296327410608526967438107789386856/21997932489, -5079183568366711688055081390151421034581406306971/3262667352971013)
(1108010900182346032057836322517097001143323594/1302148742657458835117521, -5146426397907349964313286423671529793727884361155993801967921965033/1485904486117730390218186013368345319)
(700238461844261214407999144343929335909647288924998/154582113327366840299726711569, -17868223306241676641255943568901210853545532481977488076751994056703356089815/60776944211648313140538609489813310976469497)
(677335775334740731171161159348011185784/701820218637857881, 6201596027153834036965116231975839311079563599553478823197/587947859201613357760616029)
(1084501217018405082426985496510969062646/630398083894111129, -27821665769979087769947352305187374314317180334450134863749/500521026596875096734572867)
(10874355349983855905730299811368010551/12965984734685284, -3453889967997746759088009739713534906205318991525975189/1476414354312900161020952)
(45226557715076218659469441802507062046726434519648/40849584553646528086741615249, 152483097764528567710082950357876492147442463429773619827883250445644628969/8256223976620231162790839345742468030011193)
(5540943199156068958312844291552882706063434/1062643812276969920761, -12687653545365206286344898181168948960438433348078954452315879997/34640294575633318809298879365491)
(2799006478663401815994881307536071754/3299151299421121, -616843900087049432654217555934574274374723300000040113/189497440833310909645919)
(108426447522220912275738198029728806756663386/82796852071566798202249, -716466497703461283965211354613535676175241356888482597456762626549/23824332296634644379234071006425307)
(1288613026244177838771721789517987417289251255781446/1555552559187090817851466974889, 1461006629684774696718210079428281646305362631262490014211834495275340711741/1940113039304495215671362471339796923927494037)
(12075424976948190599038883596888047565227724286/9810334047903780034572769, -783376627150835574300602094407629501202386636993319793408450329759369/30727391472210768716978737340571081647)

Commentary

2-isogenous partner of curve#519 (Matthias Breddin).

last edited by Steps Unbounded at 2026-09-26 21:36:22 UTC · history