curve #97

y² + xy = x³ − 10363235273247623603445x + 420203984207204686370404578747937

a-invariants: [1, 0, 0, -10363235273247623603445, 420203984207204686370404578747937]
rank (lower bound): ≥ 17
torsion subgroup: trivial
conductor (N): 14671894523046150637866090498215403768993465347230 ★ record for rank ≥ 17
naive height: 163.7597
Faltings height: 11.5666
discriminant (Δ): -5048330766436983365467936939800781032431719923365507757411328000000
primes of bad reduction: 2, 5, 7, 13, 613, 1024411, 19339667, 2352864853, 5453069033, 103472067337
regulator: 170247190042437.264079785742106157706972865281708359581724807739340544747
submitted by: David Renshaw
submitted at: 2026-06-23 13:32:30 UTC
last updated: 2026-07-01 22:35:39 UTC

Witness: 17 independent points

(27818223314, -12387282451487657)
(259321349714, 123172612765731543)
(46234992594, -6316291369579177)
(94745825874, -16995409414228777)
(60159528674, -3805832132220377)
(44236152114, -6952523701485257)
(-109704598486, 15388129882508943)
(115544232594, -27665228871893417)
(41433429464, 7870784808865993)
(52821878354, -4492179472932137)
(95371607394, -17300951018924377)
(57062624864, -3828168140667857)
(51138107314, -4896893849399657)
(63014091294, -4170037882068317)
(34556507314, -10166260332899657)
(42727121682, -7444193513075305)
(544874284066/9, 103516527083663981/27)

Commentary

Generated by local generalized Mestre/Fermigier quartic-family search: Mestre parameters u=-2, v=-4, specialization T=2429/5. Found in uv-smoke-5 by Nagao stage-1 sieve (M=200, m<=5000, n<=12), rescored at M=1000, selected by exact minimal-height triage, and certified with famcert from quartic-side rational points.

last edited by David Renshaw at 2026-06-23 13:32:30 UTC · history