curve #4321

y² + y = x³ − x² − 1774897982859587528250x + 27161891006732216692105002491406

a-invariants: [0, -1, 1, -1774897982859587528250, 27161891006732216692105002491406]
c-invariants: [85195103177260201356016, -23467873829305464602915160944438936]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/5ℤ
conductor (N): 5886444423733736980645
discriminant (Δ): 39133375789501649216531428085233976313021291701839519468105403125 ☆ record for ℤ/5ℤ torsion, rank ≥ 7
Faltings height: 11.1451 ☆ record for ℤ/5ℤ torsion, rank ≥ 7
naive height: 158.3977 ☆ record for ℤ/5ℤ torsion, rank ≥ 7
primes of bad reduction: 5, 11, 19, 43, 59, 107, 179, 115925634521
regulator: 599366.0262130618575958628425895546044041731319068033
submitted by: Volkan Dagli
submitted at: 2026-10-17 09:50:28 UTC
last updated: 2026-10-17 09:50:28 UTC

(9597604695, 3318312177071402)
(52651304925/4, 19725814118996421/8)
(-11942476868459/625, 114926082737125159536/15625)
(138517715575/9, 50443432097669999/27)
(7881198559825/144, 16750232084940697711/1728)
(35192515738057/841, 124755515212508903271/24389)
(5233853624097975/279841, 105548385753774718145418/148035889)

Curve 5-7.ec from Layr Labs / Yukon Elliptic Rank Challenge with conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 09:50:28 UTC · history