curve #1962

y² + xy + y = x³ − x² − 186813716938553342309885355902x + 32157571671558600483620819979557956236841229

a-invariants: [1, -1, 1, -186813716938553342309885355902, 32157571671558600483620819979557956236841229]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 34859340601273694421986298589699335912930871519323215803010610
discriminant (Δ): -29475743542078390696777831379773813615617151384256962923243675591968633764393136947200000
Faltings height: 15.7433
naive height: 213.8816
primes of bad reduction: 2, 3, 5, 7, 11, 19, 37, 41, 43, 73, 101, 3733, 6823, 246643, 7965980176577402835373050705339763
regulator: 48639763062465725.22372692099428792098223410697795995465449167542072655084282
submitted by: Ritik Jain
submitted at: 2026-09-25 20:06:53 UTC
last updated: 2026-09-25 20:06:53 UTC

(112227939444485129433/833569, -2339072362528247467910963773133/761048497)
(5027357400231187/36, 640492228500648669743371/216)
(174580565460351409/441, 41667131073540348726424103/9261)
(968530177124223/4, 8465189152485136961123/8)
(291395930508937653/1849, -204729431955756739844585903/79507)
(282682433186937, 1391972336009588232931)
(-464250651601863, 4338967523632639844131)
(96441361549971585347357304777/34131365699991121, 35463228724351991243971472493160062985298469611/6305659261579857333509081)
(1728331722744431203/7569, 780784817491287767915007143/658503)
(1562029255294137, 59595297251594841821731)
(706860244472231521/2025, 280571264185487123890386559/91125)
(24670823006796673/9, 3829622718677444048341937/27)
(166162427782407, 2388281233016449174981)
(105803309519097, -3684624919569683096669)
(-49645102680947487/169, 17255349674251990535599327/2197)
(-343818527291463, -7466216740980813435869)
(-4498876837793663123140887691797/9294128983159969, 2712814730836667899654145626283503456392104407/896010384280645910492047)
(3816812160960149969200363781678713/15988307281025888449, 69012028144518929587201846659097700526233069717117/63929856505186635133789610207)
(9059202030949530696132148833/58645745118601, 1187040034200516591771976447266253189445393/449112107051247506651)

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