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curve #5771

y² = x³ − 40074800825472936627

a-invariants: [0, 0, 0, 0, -40074800825472936627]
c-invariants: [0, 34624627913208617245728]
rank (lower bound): ≥ 7
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 12984235467453231467148
discriminant (Δ): -693787533638972988766306307156564315239728
Faltings height: 6.7075
naive height: 103.7977
primes of bad reduction: 2, 3, 13, 19, 37, 47, 67, 127
regulator: 14354685.24701713246952780343776525406960856693639877
submitted by: Maksym Voznyy
submitted at: 2026-10-25 01:32:35 UTC
last updated: 2026-10-25 01:32:35 UTC

Witness: 7 independent points log in to add more points →

(305672233/36, 5166324835595/216)
(77763751, 685720756318)
(474651532864327/7230721, -10340262529457233429706/19443408769)
(2844277903/729, 86511112749082/19683)
(920010774549451/31013761, 27884043825690636705992/172715635009)
(33005079330149329/6849217600, -4803873697745147035157017/566841248576000)
(7996471561/576, 709693190586523/13824)

Commentary

Voznyy (2026), A = -65788133346, [r, s, t] = [26, 36, 47] for S2 in https://arxiv.org/pdf/math/0403116

last edited by Maksym Voznyy at 2026-10-25 01:32:35 UTC · history

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