curve #4015

y² + xy + y = x³ + x² − 1019188320158889761182807255392605145x − 295790089424260751575358162347115559511838112969284505

a-invariants: [1, 1, 1, -1019188320158889761182807255392605145, -295790089424260751575358162347115559511838112969284505]
c-invariants: [48921039367626708536774748258845046961, 255562637262561288994201657010707529392417517664123959959]
rank (lower bound): ≥ 16
torsion subgroup: ℤ/2ℤ
conductor (N): 2774700096374548868697941163846920764265826133256711902170
discriminant (Δ): 29958854757518946016041896408200379479894420610475509031599914246970973637374994914558963432368517201239040000
Faltings height: 19.7160
naive height: 260.3498
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 29, 43, 211, 349, 1279, 1321, 1381, 2549, 15767, 58601, 407521, 1204681, 19629975401
regulator: 10915521441441812653522960.05421257220538938348803226628944443771691060
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:46:18 UTC
last updated: 2026-10-05 04:46:18 UTC

Witness: 16 independent points log in to add more points →

(28429770272040172193085631/6265009, -147541140987321875197675625840194396840/15681317527)
(-64093919914267513720899107304950225/86372461229070241, 5782270536142978547179171811350353579876564860366344/25384168552109474171422961)
(-123943133331683611355020263197/305953903161, 38070123640451610153713715474013581638938108/169232588409347091)
(-1726043756526981581839680751/5189761600, 29884899433840694514131650318435069138827/373870425664000)
(-499706802304145844381848609537/657978923281, 107016615012543656152206082115942443240041752/533725525429692679)
(-1266911974346716422902190339503287/1567678580154241, -494527194961343624678915696809384237772110926402/62070541856019185968961)
(16378426989024164740762542863/2704104001, -2065345351454441998449428337390909957761112/140616112156001)
(25558100124031481522275353847/6751415889, -3926399389125816871169604780039072812759456/554743589351463)
(170639349088023168197021156261587327/2985477910783729, -70477530621429944582829614713908391508666804594671016/163125100914171151856183)
(4239557492926543045845358182338167/15547982406649, 276043683488089188813493801602136663682899496255816/61307140591780825357)
(-352834261705687076866323908296997/742246924035681, -5765038868971586442622668369148454220031967384848/20221930328035216621329)
(25002092851774958036145126040467647041523857/1640987910341211675981609, 124735715793016179073692389358992193687668325651954248511779375626/2102122749432630180614424604456237227)
(276293357714041059797076984605119845047/190303286334120044089, -2975747797838402614387833841168652469723971192156620734456/2625242535074527345173810616813)
(-6107668472347581437832465004383977901905/14923776794430496552641, -418817393742697150210443294100366549912253490474118156632424/1823132014516101053919999215081439)
(8133147377762821604937066271743376127/237614528656240849, -23184480842833620655546639188856740515270262608085383016/115826914481392627372848743)
(23928666780917165227534596614126526640309243/1431195873007202339534721, 116834416933658009392611045900439709728849791355247697410949795472/1712176818856354731217150727219811519)

Commentary

Unlisted rational-isogeny neighbor of curve#3486 (source contributor: Steps Unbounded). Source equation and witness provenance are credited to that entry. Exact rank 16: 16 independent points certified by the unchanged ICARM verifier, with a matching unconditional upper bound computed using PARI/GP 2.17.2 ellrank. This is an additional representative of a known isogeny class, not a claim of a new world rank record.

last edited by Odbayar Shinebayar at 2026-10-05 04:46:18 UTC · history