curve #36

y² + xy + y = x³ + 34318214642441646362435632562579908747x + 3184376895814127197244886284686214848599453811643486936756

a-invariants: [1, 0, 1, 34318214642441646362435632562579908747, 3184376895814127197244886284686214848599453811643486936756]
c-invariants: [-1647274302837199025396910363003835619879, -2751301637983405898417110838514633830651832727715466959927581]
rank (lower bound): ≥ 15
torsion subgroup: ℤ/2ℤ
conductor (N): 8754566324589342390719388201154487417353298842735433399274068130
discriminant (Δ): -4383177432172452900429407516665453934052428354033391150708350854907555007169944896851345195235905604109325415039062500
Faltings height: 21.2524
naive height: 278.3344
primes of bad reduction: 2, 3, 5, 7, 11, 17, 67, 89, 139, 211, 281, 431, 443, 577, 647, 977, 1613, 3863, 10567, 11923, 15361, 73277
regulator: 26441299746981574.028361312934843803735096979068358730331594461979348
submitted by: David Renshaw
submitted at: 2026-05-27 22:12:14 UTC
last updated: 2026-07-01 22:43:36 UTC

(-5955399047526089895, -52619192486073556789679851928)
(4996845231479851005, 58996807068911558580932032822)
(-13155206566829859045, -21360729170232157127198638028)
(5982316535030750730, 60031451151089353115173694947)
(3520990345094746477605, 208928587539794577855401843236822)
(-149780582516304339030/289, -276460561394858085500066301116014/4913)
(5537764707520796477505/256, 485495189997228202630782626087287/4096)
(10379720384859947873670/529, 1299762167535132813050160826170149/12167)
(3607902715536254330407755/36481, 6876286874413935169019164791798028712/6967871)
(575451914344737045120/18769, 145126149873708232941281933935318916/2571353)
(-635343181823720560310/81, -35955391603910411255538526302302/729)
(385275433846822770303250/9, 239142619084196570639847351097336094/27)
(11630065797764473356485380/349281, 41921913401808378926412528792277717237/206425071)
(2130862087205394565011555/206116, 6377017660319811010371576798520557433/93576664)
(361886218060793196368152192851/82159049956, 1377397812507014979022748799194701395570639671/23549577125088104)

Found by Dujella (2002). A curve of rank exactly 15, via Dujella's elliptic-curve rank-records tables.

last edited by David Renshaw at 2026-05-27 22:32:08 UTC · history