curve #4194

y² + xy + y = x³ + x² − 15492708048666807434281x + 654751424202516470217616506141719

a-invariants

[1, 1, 1, -15492708048666807434281, 654751424202516470217616506141719]

c-invariants

[743649986336006756845489, -565705230516551605165540711982786537]

rank (lower bound)

≥ 18

torsion subgroup

trivial

conductor (N)

387757907717933562317496501686118091598334832547665790460690

discriminant (Δ)

52793642404020681160431958900926731733928549719590546943645022617600

Faltings height

11.7236

naive height

164.8976

primes of bad reduction

2, 3, 5, 277, 65203, 48796859, 14665612089005521086866580401535799189085387

regulator

143095283691347070.30568903090118902892094945848209897345463230032550469838

submitted by

Andrii Prokhorenkov

submitted at

2026-10-12 04:10:57 UTC

later contributions

(2461848549959, -3857854951605027960)
(470576605957207/169, -10198067677467548809256/2197)
(449814843169878311/361, 301682879883809853807098952/6859)
(2397286307337/64, 5769653001091766543/512)
(-33562600303705441/243049, -1520039229981473653181400/119823157)
(13964403830625791/277729, -248581776680613650879160/146363183)
(-11242103219505257/139129, 1927145274434588836609912/51895117)
(2139587578542071/7225, 91166084173969965056664/614125)
(242737607028778039/2595321, -20438026295788592844605560/4181062131)
(43475911693234559/192721, -7864228058403603364424280/84604519)
(118871005199, 22199095893053400)
(1020122145999008634347687620991/373004257603155025, -1029283731742162017012169589129134729193571624/227808898176722814318993625)
(1061040878159, -1085700486031910760)
(1129536108303, -1193430863427625448)
(268173773903, -125643729758388456)
(2296882745662031/9409, -97533065805894404853480/912673)
(-173712416164969/1225, 16009980711844980216/42875)
(34842090373271/121, -188557984063967858232/1331)

Mestre split-sextic roots (0, 13, 1568, 1581, 1700, 1756), primitive shift T=89/2.

last edited by Andrii Prokhorenkov at 2026-10-12 04:10:57 UTC · history