curve #428

y² = x³ + x² − 24917238940622813301347573754793308x + 1527468176676160166289505293787711918102662665461488

a-invariants: [0, 1, 0, -24917238940622813301347573754793308, 1527468176676160166289505293787711918102662665461488]
rank (lower bound): ≥ 21
torsion subgroup: trivial
conductor (N): 446480526610737179355955961227189254020824567046961876711405982701219954637800
discriminant (Δ): -17823187605965034199768344802638363317494960253584381536607303619622147560661226461773809327050839520000
Faltings height: 18.6294
naive height: 249.2340
primes of bad reduction: 2, 3, 5, 7, 11, 13, 31, 47, 61, 73, 101, 11939, 5568285957643, 2437788650277983056207690736085794602381810177
regulator: 341674714485273844622.94545361261494334321481368766421980681514238687641058712867
submitted by: Bhavik Mehta
submitted at: 2026-08-30 01:39:34 UTC
last updated: 2026-08-30 01:39:34 UTC

Witness: 21 independent points log in to add more points →

(57933032599511022, -16684540924439275616791062)
(85950447340642068, 4558234550645150694659340)
(91702112382409944, -3695028238772283457329516)
(87820169412135828, -4066293041805435364097460)
(162330140076881268, -41955010236825509981882340)
(-144408146282779272, -45981240376955693077574460)
(27286357460584744398, 142531578686178878956461958410)
(327051983255582397/4, 48504699838226895801382845/8)
(34875168603019698, 26474386609952499427118910)
(122574460162343142, -17744600056793831151232302)
(1160916650133925638, -1239838654304331011218898610)
(109299386386024788, 10476574609858392308413140)
(90800630131556298, -3687285920663102227560090)
(175670270818256343, 50709391236220297036310910)
(186733496773008138, 58188227253028711539811110)
(41092139179916778, -23936420556125255023135290)
(83509732602785442, 5387270987570753075196402)
(105704389646328888, 8642104589468300324464860)
(104620427215829478, 8107524463592025313631790)
(153798722176767348, 36512886240471431017658340)
(189459276261035448, -60060571420582630886042340)

Commentary

Found by specializing Noam D. Elkies's rank-17 elliptic K3 fibration (arXiv:2608.25406) at t = 13/6. The 4 points beyond the seventeen generic sections came from searching the 1311 norm-4 quartic covers of the Mordell-Weil lattice; the claimed lower bound is rank >= 21.

last edited by Bhavik Mehta at 2026-08-30 01:39:34 UTC · history