curve #6247

y² = x³ − 6444421059559x + 6276680644075449226

a-invariants: [0, 0, 0, -6444421059559, 6276680644075449226]
c-invariants: [309332210858832, -5423052076481188131264]
rank (lower bound): ≥ 15
torsion subgroup: trivial
conductor (N): 3425148201540012310824333672243640232
discriminant (Δ): 109604742449280393946378677511796487424
Faltings height: 6.1592
naive height: 100.0963
primes of bad reduction: 2, 2118581, 49857403, 4053355119576273177203
regulator: 331240508506.34026460712033388843362433100582229131306753708301476660
submitted by: The Wren
submitted at: 2026-10-31 22:39:35 UTC
last updated: 2026-10-31 22:39:35 UTC

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

(205667647/169, 1068132770548/2197)
(84604237, -777848164214)
(-14153239/25, 390184488866/125)
(963817501/625, -1207268773126/15625)
(2331968545/1521, 794748466234/59319)
(60611982/49, -152544160448/343)
(2546179477/1849, 9285299324558/79507)
(122634570795/1681, 42920007952631444/68921)
(9321347773/121, 899466761884954/1331)
(-2881287, 961767266)
(1545435, 91194044)
(1917925, 985763326)
(2015847, 1215478724)
(2107297, 1433264326)
(4071833, 6895386046)

Commentary

Jacobian of a genus-one curve from J.-F. Mestre's ten-point construction. Rank 15 proven (independent generators plus a matching 2-descent upper bound) in M. Rubinstein's elliptic-curves-by-rank collection, file mestre/mestre_rank_15.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by The Wren at 2026-10-31 22:39:35 UTC · history