curve #3940

y² + xy + y = x³ − 379712400221393389924078x + 91443227117108044028905790291214048

a-invariants: [1, 0, 1, -379712400221393389924078, 91443227117108044028905790291214048]
c-invariants: [18226195210626882716355721, -79006948229208689333790543135683471269]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/6ℤ
conductor (N): 447060738391164495290
discriminant (Δ): -108484768455546788682304270418676352300282576326608329258354984375000000
Faltings height: 12.4270
naive height: 174.5252
primes of bad reduction: 2, 5, 7, 11, 31, 41, 43, 59, 61, 73, 109, 409, 907
regulator: 2444359232.244308850416737389742798360575782223885271
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:30:34 UTC
last updated: 2026-10-05 04:30:34 UTC

Witness: 7 independent points log in to add more points →

(404857085354125509/547600, 187822256723574443761561047/405224000)
(1422679046575652302726/4445555625, 15406319856118804868223647876324/296407421296875)
(1356159919758462525274/3616218225, 9191044613295122746597964073212/217461282960375)
(-17694554972215031261316/167836883041, 24820414787675096442211425872497800/68759246407353839)
(6307093439868065165014779/15174811176196, 4352994419065308196026368563066436825/59113264489515051256)
(513331483338893023619346/118111130929, 364278769631746303107167868806410900/40591606699762217)
(481662185874737084108766/2778899002009, 813457153903470263485705369365502900/4632432973046009027)

Commentary

Unlisted rational-isogeny neighbor of curve#3717 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 7: 7 independent points certified by the unchanged ICARM verifier, with a matching unconditional upper bound computed using PARI/GP 2.17.2 ellrank. This is an additional representative of a known isogeny class, not a claim of a new world rank record.

last edited by Odbayar Shinebayar at 2026-10-05 04:30:34 UTC · history