curve #6413

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y² + xy = x³ + x² − 107554267611487x + 3640215063248712616105

a-invariants

[1, 1, 0, -107554267611487, 3640215063248712616105]

c-invariants

[5162604845351401, -3145145853366424040450165]

rank (lower bound)

≥ 17

torsion subgroup

trivial

conductor (N)

940812709412034880430328371679874986264672318

discriminant (Δ)

-5644876256472209282581970230079249917588033908 ★ record for rank ≥ 17

Faltings height

7.4590 ★ record for rank ≥ 17

naive height

112.8158 ★ record for rank ≥ 17

primes of bad reduction

2, 3, 6863, 1525669352583047807, 14975368023564927710533

regulator

157005671536158.412829275422375393089676407911733800859195301430676511154

submitted by

The Wren

submitted at

2026-11-02 13:28:04 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-11-02 13:30:52 UTC

Witness: 17 independent points log in to add more points →

(2947936, -57870036275)
(5396776, -56720869571)
(-1855796, 61915566919)
(-2272178, -62231224673)
(9022462, -58350743093)
(-6200210, -63783434045)
(-8284226, 62954009707)
(-9870788, 61161500407)
(13112788, 66960301405)
(-14295776, -47492015981)
(-17629106, 7587248287)
(16829824, -81230489843)
(3603649, 57438822019)
(1391953, -59104008365)
(886873, -59544760148)
(-2946251, 62703325732)
(9190753, 58544980387)

Commentary

Original find by the Layr submitter, posted to the Layr Labs Elliptic Rank Challenge public repository: submission/board/1-17-m10-121112.ec, commit ee5456a (Validate submission a7719040-5417-4459-bf2c-8fa1cc09f72c, 2026-11-02 12:11 UTC). Mestre ten-root construction (file series m10). Rank lower bound 17 from the 17 supplied points as posted.

last edited by The Wren at 2026-11-02 13:28:04 UTC · history