curve #3204

y² + xy = x³ − 4562085945883852510841543387549451275x + 3745932842931265406265852327213395046483588868755572721

a-invariants: [1, 0, 0, -4562085945883852510841543387549451275, 3745932842931265406265852327213395046483588868755572721]
rank (lower bound): ≥ 15
torsion subgroup: ℤ/2ℤ
conductor (N): 7210387210131632436261753944550733665686372892278111682534
discriminant (Δ): 14906347248414438753898124914643480664529482567971408560030701023896763582543554633815966401020735919313825792
Faltings height: 19.8515
naive height: 264.8461
primes of bad reduction: 2, 3, 7, 17, 19, 23, 29, 103, 107, 113, 241, 311, 367, 569, 743, 2731, 4027, 18539, 30931, 83891
regulator: 17053990674136615.800146244787405380105822648342358960093110598568229
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:42:33 UTC
last updated: 2026-09-26 20:42:33 UTC

Witness: 15 independent points log in to add more points →

(1185670516548425254, 60290420205775826394371881)
(1554321264148312594, 640385095371248235429151561)
(1293507567454295806, 95329079037031587947012161)
(1194410272462791934, 29920057751113875403314625)
(1765415189937321430, 1092799287332515989409668049)
(1359944139997096630, 238530608278523772792626449)
(1268274168995901694, 803407511955856542413761)
(793112856142726942, 791564288933005478426171809)
(-2463270085030832162, -192872978664982906262683967)
(1195935897826785646, 21747727978699644235464433)
(5906688287408888524, 13523215707481836000826510705)
(3249716208080624692, 4820744892134994527136441259)
(1146058813103733988, 151016246821093755237086683)
(-257979112036754762, -2214878412585172045518930671)
(777239190765714276539326/483025, 253758777295151476729268215096353191/335702375)

Commentary

Dujella (2009). Source: https://dujella.github.io/tors/z2old141516171819.html (curve entry 46). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:42:33 UTC · history