curve #5547

y² = x³ + x² − 8604258110076365717930946985x + 299722697449892767847148224816203703037275

a-invariants: [0, 1, 0, -8604258110076365717930946985, 299722697449892767847148224816203703037275]
c-invariants: [413004389283665554460685455296, -258960410596709829446271768234526763536937344]
rank (lower bound): ≥ 20
torsion subgroup: trivial
conductor (N): 306097343812929710376149520274032857791488284468589478234963320
discriminant (Δ): 1959924070966741819099160944272572188071412166377721017152383053801866865853940000000
Faltings height: 14.9535
naive height: 204.5798
primes of bad reduction: 2, 3, 5, 11, 13, 19, 23, 29, 43, 13055435032943, 555164434209439, 105029898935842244678263
regulator: 407259806593921736.440168173204396228666031514678006924850664459025018674179845
submitted by: apkorte
submitted at: 2026-10-23 00:59:32 UTC
last updated: 2026-10-23 00:59:32 UTC

Witness: 20 independent points log in to add more points →

(32028253551005, -238742976119884735950)
(176160949059455, 2061731015147557074750)
(26094050608205, -304910111828366442750)
(33211131370205, -224937190522236084750)
(82015275215189, -381730650555522027210)
(42417172910615, 105223919619338000910)
(32277093995363, -235857742471651963806)
(202088498697005, 2610392143525127532450)
(14243584923455, 424331180512682429250)
(2751211486955, 525424959507488147250)
(36596846881955, -183981538698321185250)
(111006199405175, 844071600849690714930)
(-25760791555645, -710126652305299744350)
(60896722948925, -39769890899200985070)
(70925157661055, 215045777494604563650)
(-40039053551995, -761604496155122998950)
(11208685608909005, -1186635142356685996882050)
(68697864030155, 181220871638047720050)
(1608289967615405, 64393004082783521123550)
(46179557491955, -29362414261263954750)

Commentary

Specialization at T = 47/11 of the rank-17 fibration of X1008 given in curve#3589. Found by Claude (Anthropic): a Mestre-Nagao sieve over the fibration, then a 2-covering point search seeded with its generic sections.

last edited by apkorte at 2026-10-23 00:59:32 UTC · history