curve #4283

y² + xy + y = x³ − 91674219518569767828x + 332054142572796459708583319362

a-invariants: [1, 0, 1, -91674219518569767828, 332054142572796459708583319362]
c-invariants: [4400362536891348855721, -286894779189496684993553011212565]
rank (lower bound): ≥ 12
torsion subgroup: ℤ/2ℤ
conductor (N): 367232800181284030614030562194142782
discriminant (Δ): 1676182610777024805087875556853268381482352608100892390759312
Faltings height: 10.3481
naive height: 149.5079
primes of bad reduction: 2, 3, 11, 37, 53, 127, 137, 173, 347, 359, 733, 1039, 1361, 1493, 1543, 3169
regulator: 1962094449348402.2216829578217914783875288634959073449739222734
submitted by: The Wren
submitted at: 2026-10-16 16:05:32 UTC
last updated: 2026-10-16 16:05:32 UTC

Witness: 12 independent points log in to add more points →

(230303116053871721/1081600, -110412478842265384071050739/1124864000)
(5167602101201/256, -10607605217729861967/4096)
(1979527396037/169, -2043682523133137145/2197)
(6910453961, -168965201752245)
(1591052624153/256, 199056676421533851/4096)
(9905066626, 629124917185130)
(46375500821714/49, 315798858655488055590/343)
(997746005342177/64, 31515910583825801453877/512)
(129897607964555255786/23088025, -1480475393883958500043434946881/110937960125)
(775707712532657/73984, -14559867675642188338047/20123648)
(55157258052026/9025, -6447677341783024011/857375)
(1114174825076549/64009, 32430023958482173266135/16194277)

Commentary

Obtained by a 2-isogeny from a specialization at T = 82 of the family associated with curve#802. PARI/GP returned rank bounds [12,12]. Twelve rational points are supplied.

last edited by The Wren at 2026-10-16 16:05:32 UTC · history