curve #4016

y² + xy = x³ − 96530126249183520881665099622230863x + 2807044289365975553937744183998600954453672848844217

a-invariants: [1, 0, 0, -96530126249183520881665099622230863, 2807044289365975553937744183998600954453672848844217]
c-invariants: [4633446059960809002319924781867081425, -2425286266012202885552380064916004728127860514202025625]
rank (lower bound): ≥ 16
torsion subgroup: ℤ/2ℤ
conductor (N): 4037723001611237548976485813408801349432131894744731730350
discriminant (Δ): 54162394123530447580495431211861592641810856611752338287754644006540014584740860107365739415831494229000000
Faltings height: 19.1711
naive height: 253.2791
primes of bad reduction: 2, 3, 5, 7, 11, 19, 41, 71, 79, 97, 151, 163, 179, 191, 193, 199, 239, 811, 1481, 2179, 21563, 392599, 438143597
regulator: 399963582110715549094135.0263788557559309444176558671744528184940495006
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:46:28 UTC
last updated: 2026-10-05 04:46:28 UTC

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

(-7105362832321028105082/22201, 100268890496448143625511487342673/3307949)
(-614369822703161280465318/2468041, 414181996909057787459204845701951639/3877292411)
(-12353346368233147995918/73441, 2378738543287396072386135734792139/19902511)
(1036679554974304734928662/2211169, -809443080191528589922764630911881365/3288008303)
(125541706601867236672899/386884, 18090969462881509425228308991509157/240641848)
(501847207962575734758/841, 9684892748914502194165041442185/24389)
(-1490827542485623242869876523/47927717776, 797679828878370945997541117260007470998201/10492527686393024)
(-3926786670730567232901282444/44909662561, 978881409351463034637371832278578788911091/9517210780264559)
(-187928673333035798342634/4289041, 740645641813490832732969340127596755/8882603911)
(18912837763813994553/64, -4794559726244801972698095087/512)
(19770951147621553898765056758/66552132529, 320384343939050750624900365848873638626317/17168919493433833)
(419034589192420139604593928/14827689361, -18203536215672747422241608693402758419045/1805552905799609)
(-467395083932018171355961863712202/11203927603840449, -97515508429899706867729184930520460987032401379893/1185920129795359376904543)
(2276483786689133105945868/923521, -3407695600544965411591571444296101273/887503681)
(179916621814596275162266438/236759769, 2210796680776109523262984736991648306047/3643022565603)
(-1474148834151299575062877264308792/13864891292028529, -177857258204470992026448353437037062692776345210067/1632580869860389985009417)

Commentary

Unlisted rational-isogeny neighbor of curve#3654 (source contributor: Michael Rubinstein). 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 04:46:28 UTC · history