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curve #6360

y2 + xy = x3 − x2 − 714386133431727088839x + 5426117607676515594095147180489
a-invariants
[1, -1, 0, -714386133431727088839, 5426117607676515594095147180489]
c-invariants
[34290534404722900264281, -4688165612878202068476954112753245]
rank (lower bound)
≥ 19
torsion subgroup
trivial
conductor (N)
76991372034934662082752207026504149892549792743154890708806
discriminant (Δ)
10614184531480162384052384765087915112486699527156819542897412772
Faltings height
10.9941
naive height
155.6675
primes of bad reduction
2, 3, 23, 37, 671647, 1406933179, 17554241580971, 303000518962990801080302879
regulator
311222932419488395.5357994252437171647964491465267835102096028004066273766345
submitted by
The Wren
submitted at
last updated

Witness: 19 independent points log in to add more points →

Commentary

From the Layr-Labs elliptic-rank-challenge-public repository, submission/board/1-19-m10-kh-b2.ec. The source credits its “kshitij-hash lane” with this find using Mestre's ten-root construction, with roots [0,7,38,64,65,73,75,86,105,125]. The displayed model and all 19 rational points are reproduced from that source. All points were checked exactly on this model, which was independently confirmed minimal. The minimal discriminant was fully factored and every bad-reduction prime proved prime. The source describes the rank as certified 19; no matching upper-bound certificate is asserted here. Source at commit 140b9d566eeaefe70e423bca75e3c5f091b0eaab: https://github.com/Layr-Labs/elliptic-rank-challenge-public/blob/140b9d566eeaefe70e423bca75e3c5f091b0eaab/submission/board/1-19-m10-kh-b2.ec

last edited by The Wren at · history

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