curve #6329

y² = x³ + x² − 32294401259964911x − 1725293338485739495016015

a-invariants: [0, 1, 0, -32294401259964911, -1725293338485739495016015]
c-invariants: [1550131260478315744, 1490653435150891360823942528]
rank (lower bound): ≥ 12
torsion subgroup: ℤ/2ℤ
conductor (N): 562432500597433744639469518241920
discriminant (Δ): 869660576556062388193774936136010900347200665440000 ☆ record for ℤ/2ℤ torsion, rank ≥ 12
Faltings height: 8.4863 ☆ record for ℤ/2ℤ torsion, rank ≥ 12
naive height: 125.6546 ☆ record for ℤ/2ℤ torsion, rank ≥ 12
primes of bad reduction: 2, 5, 11, 31, 47, 89, 97, 191, 617, 769, 823, 1367, 2777, 22433
regulator: 27102055932.266890772139353754816590706802797274432989686369436
submitted by: The Wren
submitted at: 2026-11-01 01:10:28 UTC
last updated: 2026-11-01 01:10:28 UTC

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

(-74041568, 509830865225)
(205540911, -566026943504)
(742622401, 19591822955474)
(-98786639, -707759120854)
(41691717832, 8512765009714475)
(66497169897/121, -16110377765262850/1331)
(430909980429/2116, 36860640985321021/97336)
(-2012025215/16, 37711760818985/64)
(47764061736, 10438757271772229)
(1509691562737/6241, -1059457141684930150/493039)
(-122681776, 624643959039)
(1410229751, 52510224817524)

Commentary

Rank 12 curve with rational 2-torsion (torsion Z/2) from Layr-Labs elliptic-rank-challenge-public, file submission/board/z2-r12-s.ec, commit a066c9ff5312fb736e666731855b7cc6b39dabc1: https://github.com/Layr-Labs/elliptic-rank-challenge-public

last edited by The Wren at 2026-11-01 01:10:28 UTC · history