curve #1918

y² + xy + y = x³ − x² − 184499078723795351292402856849265045735050014057471578105x + 964453138489564009753345308467213074059220517883096279979317728176086605791569407897

a-invariants

[1, -1, 1, -184499078723795351292402856849265045735050014057471578105, 964453138489564009753345308467213074059220517883096279979317728176086605791569407897]

rank (lower bound)

≥ 13

torsion subgroup

ℤ/4ℤ

conductor (N)

2409091324418488847528892674329981342840728238071834873259259850

discriminant (Δ)

107872879475709798421113808538619644825539721822581780208321212992172791688116147651756537468376005227075059898874931452643948492495469908455649978576103874232320000000

Faltings height

31.0620

naive height

400.2853

primes of bad reduction

2, 3, 5, 11, 13, 19, 43, 71, 89, 101, 113, 137, 197, 271, 397, 401, 563, 1087, 2311, 1576391, 2205527, 110976062006309

regulator

2420226180809469.757677531444945988688431046544409785233662383345

submitted by

dujella

submitted at

2026-09-25 18:59:38 UTC

later contributions

primes of bad reduction recorded · dujella · 2026-09-25 19:01:21 UTC

Witness: 13 independent points log in to add more points →

(7418352899754542002943351239, 63406316661285351331864627295671267054380)
(7286937435690559834493694759, 83380557155352348480312965602823251681420)
(8037226651605469079356275909, 27803852934375457248797010898116969096970)
(70594220244765751149904359, 975412180414299465471847572346217983163020)
(-15150446782016794020242767641, -531152603661737065821842721173593751691380)
(4580987484186293888529481959, 464111231280810991878992761972220074254220)
(7715831643760301910832693509, 15622959943417757044865134109639017460170)
(7297441578037124868028579209, 81792534573736410869729303627374153838320)
(647230548488490804676664166679/81, 14422769082216109590544410090151354658788780/729)
(4084165098248306300189178589, 528255588322186869887672878165776482675280)
(1381338270999194880352191971559, 1623413482664505888468114703672093496102363020)
(8594988189780810279566435559, 116749146919433564970236535528450528193420)
(3278964307389947632795365271473, 5937468430761268981169399541683914667468744080)

Commentary

found by Elkies - Klagsbrun (2020)

last edited by dujella at 2026-09-25 18:59:38 UTC · history