curve #3875

y² + xy = x³ − 30990025086116594755952126655229787330297604920x + 2099768672095884496652177854165208259234378372964952638285482510491712

a-invariants: [1, 0, 0, -30990025086116594755952126655229787330297604920, 2099768672095884496652177854165208259234378372964952638285482510491712]
rank (lower bound): ≥ 19
torsion subgroup: ℤ/2ℤ
conductor (N): 2155758992663991692041802618212395866297853180989658043025602632708992617830 ☆ record for ℤ/2ℤ torsion, rank ≥ 19
discriminant (Δ): 83799075304235943673897955850038663830036927776899728102380384504614630970112000748298751677021908178988441318885184567418073710000000000 ☆ record for ℤ/2ℤ torsion, rank ≥ 19
Faltings height: 25.3807
naive height: 332.7636
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 43, 59, 61, 67, 307, 461, 659, 769, 773, 1153, 1487, 1609, 8521, 84827, 176597, 261059, 410741, 2959403, 5976301
regulator: 2776683489772928610536621951.049791634062424213782229614341838586986708293221
submitted by: jesper-petersen
submitted at: 2026-10-04 07:33:50 UTC
last updated: 2026-10-04 07:33:50 UTC

Witness: 19 independent points log in to add more points →

(406185852890315157460864, 237754963607715027965460666413634568)
(147745830820617184979614, 27317400504656478605139441950222068)
(3003413269576108379208322986/24649, 44588742459152270517141541043151266262474/3869893)
(103399565421682202542114, -952318687521655772736739184514182)
(196013314333816964599678, -59635406414909754989486699045273714)
(1447007511130743842209758098302581174304/11708001523983361, 15899066928802661970521312201180692973970357235516600492712/1266846965352362557647359)
(23521283920395389528370399856/729, 3607323455748504888464324993744376552021944/19683)
(12191545994881957051726116529/20736, 1291643674087948606897765320408178369754287/2985984)
(40327099790729208322763254/361, 38747078532154945927767792367379807362/6859)
(856260189265243565596046532139672/7300506249, -5525898408762051571749554450185511025332590813088/623777155433307)
(300847780276640994668429150146/2948089, 377952325870051345085478275102811248795284/5061868813)
(66419310195881713062562429545580790176/592976217316609, 84049049536627453207238858692089365230471434457224322936/14439624944427129369727)
(16623999710655909557038014276/162409, -22023326454344069096743439014457117278164/65450827)
(130352899640571679533320843698/1256641, 1606594027510800493268435944072077394022756/1408694561)
(27125633239668207404890350381461176/254920980609, 340628083750896264865293353253157461913294489293064/128708838346542273)
(3432813379497352999332577842549856/30634450729, -31354459458586819862482414878957893962766352918056/5361856007744683)
(3397901280961186312039583594485744/28954765921, -43830651629781431685568482810713755511060994282392/4926971923883281)
(14030058908397327227091236055751723864/88559298254025, -28462955516620943182242172326688170244875156685701727528/833395689352836394875)
(285450281531675665063926046702776/2337432409, -1320288495553152094893721938958633856665595838336/113007844677923)

Commentary

2-isogenous to curve #3553.

last edited by jesper-petersen at 2026-10-04 07:33:50 UTC · history