curve #4541

y² + xy + y = x³ − x² − 13551501341348644165879757x + 18962906959688379077376292302963492981

a-invariants: [1, -1, 1, -13551501341348644165879757, 18962906959688379077376292302963492981]
c-invariants: [650472064384734919962228321, -16383951613167832398563385242620627908369]
rank (lower bound): ≥ 21
torsion subgroup: trivial
conductor (N): 979177535818370910552262900218704219080193176433652068537523090 ★ record for rank ≥ 21
discriminant (Δ): 3929343632842177421542408016339296229648752905644772659584261352310504960000
Faltings height: 13.3096
naive height: 185.2192
primes of bad reduction: 2, 3, 5, 19, 29, 109, 3320881, 627001051421865887483759327603646432717018489137
regulator: 5631617052689609624.9741593943357603381651076084314557508149525269811971882478885
submitted by: Matej Jurasić
submitted at: 2026-10-17 12:09:57 UTC
last updated: 2026-10-17 12:09:57 UTC

(3301478393711, -3195035115752746536)
(2600824093811, -1144795467088820076)
(1842516567791, -499140651466729896)
(-1971664569709, 6165806087766730104)
(2325618886031, 159362259513381624)
(2926448882231, 2089864760938898544)
(3714846232775, 4459409299178936352)
(-4233096726799, 688773442113589314)
(1675656027911, -979897665376488936)
(827047013831, -2884594664583749856)
(-2723077613341, 5972661014288978616)
(4419973306031, -6739064182661347656)
(-4194846081649, 1412014868510281464)
(1734903347759, 821113926024672024)
(609209839775, -3306554263793883528)
(1707594862991, 895306334555078904)
(-1563079986801, -6027108036511125256)
(11288425990031, -36117254579188363656)
(106049605835741/16, -949976701738521659679/64)
(1680272211161, -967798895583751686)
(176598335434481/121, 2015705861537237541444/1331)

Specialization at T = -20/13 of a rank-16 fibration of X1008 (two neighbour steps from the one in curve#751).

last edited by Matej Jurasić at 2026-10-17 12:09:57 UTC · history