curve #6372

y² = x³ − x² − 6473841931837579385x + 4275955040079115505798210781

a-invariants: [0, -1, 0, -6473841931837579385, 4275955040079115505798210781]
c-invariants: [310744412728203810496, -3694425152763889320640431251840]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 98604798131699903972915030384706682823384424470877778872
discriminant (Δ): 9466060620643190781399842916931841551044904749204266771712
Faltings height: 9.8286
naive height: 141.5565
primes of bad reduction: 2, 3, 267671, 7942445005349047, 1932552357343601932676956591016269
regulator: 166925853806722454.1623117397733732179880193041954963412736215730068319964076
submitted by: The Wren
submitted at: 2026-11-01 19:43:38 UTC
last updated: 2026-11-01 19:43:38 UTC

Witness: 19 independent points log in to add more points →

(674175653, -14760416627862)
(338806073, -46059412460442)
(2230990793, -30614183015622)
(-1133012437, -100779119511402)
(584347149, 26315700080358)
(443123865, 38655561491034)
(-2817016759, -12577947419706)
(-1562478541, -102842860892658)
(3713401745, 177317187009834)
(-2082708397, -93407544496338)
(703954604, 8216469892767)
(2273281147, -36152051684710)
(-1722289091, -101572590705658)
(-2616313829, -57485933170054)
(5002138197, -311533844661450)
(10864440371, -1102876724972046)
(3218329044, -129519500696283)
(11500660861, 1204557888211066)
(18134438147, 2418786628151010)

Commentary

From Layr-Labs/elliptic-rank-challenge-public, submission/board/1-19-m10-a.ec, commit debf8f35561f00231e8c084c95b7d4e68337de78. The public file contains 19 rational points on the displayed minimal model. All 19 points were checked exactly. The minimal discriminant is 9466060620643190781399842916931841551044904749204266771712. The conductor is 98604798131699903972915030384706682823384424470877778872. Naive height is 141.55650727249346. Source attribution remains with Layr-Labs.

last edited by The Wren at 2026-11-01 19:43:39 UTC · history