curve #3161

y² = x³ − 2902707625457545077500107175592x + 1904597097766869546326844055645258034709879849

a-invariants: [0, 0, 0, -2902707625457545077500107175592, 1904597097766869546326844055645258034709879849]
rank (lower bound): ≥ 11
torsion subgroup: ℤ/3ℤ
conductor (N): 3026430495293399317367745836437881353533418460
discriminant (Δ): -1803585001881555849637090857160089312479689778527716534572783422477410997374367549740750000
Faltings height: 16.2573
naive height: 222.0443
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 67, 6551, 130547, 104576139001
regulator: 2502497330.50011428231951332835426790470487947932504202341633
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:40:11 UTC
last updated: 2026-09-26 20:40:11 UTC

Witness: 11 independent points log in to add more points →

(1063302229460058, 4508156633116678166625)
(-825654663146817, 61142274721662403678500)
(-68584647656817, 45862355645427412806000)
(1030369575281634, 2763900126117107202225)
(1042423080209358, 3390046797825888711225)
(-760622971612917, 60600386362297642810950)
(164575959418458, 37833038284168124572575)
(-75434443283612, 46077456339616112696285)
(696962978964658, 14834832809096935264175)
(979980554131023, 1065853725738960152280)
(973568051517558, 1181237636592991511625)

Commentary

Eroshkin (2006). Source: https://dujella.github.io/tors/z3old891011121314.html (curve entry 44). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:40:11 UTC · history