curve #1125

y² + xy + y = x³ + x² − 204436185783252342785934887233210383183371840x + 1165977772244037776901948451219544033496456897571880326934385121505

a-invariants: [1, 1, 1, -204436185783252342785934887233210383183371840, 1165977772244037776901948451219544033496456897571880326934385121505]
rank (lower bound): ≥ 12
torsion subgroup: ℤ/4ℤ
conductor (N): 229584468983534025788078945027068319227598545134330
discriminant (Δ): -40474603049862124207835755432043792557872007419869834935563222317416980472992314377691858366871099273728963619697964692792934400000000
Faltings height: 24.4028
naive height: 317.7715
primes of bad reduction: 2, 3, 5, 7, 11, 19, 23, 37, 61, 71, 199, 239, 313, 353, 383, 503, 569, 787, 1609, 8263, 159911, 210361
regulator: 50294851103473639.410548880340268335821786021748739543846165394
submitted by: dujella
submitted at: 2026-09-23 21:24:08 UTC
last updated: 2026-09-23 21:24:08 UTC

(978748421021154077677013, 968189872097011478431309250996630293)
(40938350455374318726499411487/734449, 8034798036372727657292256069809358560313049/629422793)
(-1833858234229021806425707334957/129823236, -1643957467127684520633723817507798298370057463/1479205950984)
(466652543424944830571020577/104329, 19679459405477726600184522257021115789031/33698267)
(1855357476468407776750099333857/9048064, 2521230557158903421620671041761650894499866191/27216576512)
(-3057825789598843317991399927/474721, -486854952876376400114202289959672893443583/327082769)
(1316165334856113211967439783713/19351201, 1479078000627128774872361508989894420231052407/85125933199)
(1813152158641149066379817305273/226532601, 702396508269043497895380089462203516064428283/3409542177651)
(14504830996189006898486130877/4313929, 6440066697804847094677254799511744033478569/8960030533)
(5609636083108794972298867953144693/459099749761, 218252275733512453971818858150694480104231578525237/311071758345811009)
(-4174731052256571796429970002572787/492999175321, -523817741681937590070885889786485498002950586908993/346153947960711619)
(6380415804693738957573514663666885797/274098255263569, 13629281585957393563736821264699724609670040970930713421/4537946867595440433497)

found by Dujella - Peral (2014)

last edited by dujella at 2026-09-23 21:24:08 UTC · history