curve #4141

y² + xy + y = x³ + x² − 399081217162040000565x + 2932271975048532129776925923547

a-invariants: [1, 1, 1, -399081217162040000565, 2932271975048532129776925923547]
c-invariants: [19155898423777920027121, -2533482986585600998305598398148169]
rank (lower bound): ≥ 17
torsion subgroup: trivial
conductor (N): 756855624206125019617445466192515119979543579877522270
discriminant (Δ): 353409192589304841160248455765797780183727997362329758842880000
Faltings height: 10.7605
naive height: 153.9207
primes of bad reduction: 2, 3, 5, 19, 1231, 7039, 13874583923, 17261304043133, 639846204624889455581
regulator: 502492351854766955.494586029310827856617865646764836756970077263334162887
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-11 01:07:06 UTC
last updated: 2026-10-11 01:07:06 UTC

(4900464609232407/358801, 36837123731545246220404/214921799)
(119419395747, 40722333284831016)
(1516591591, 1526602331425964)
(18067342308703/169, 75537429528396485372/2197)
(1678142535, 1505749051005996)
(-14090641844981/625, -10716593759154060028/15625)
(124145735263/9, -6156315541396508/27)
(-204944487617/9, 12427987812437252/27)
(18068176135, -1272848679493204)
(23782940187, 2625488051759936)
(9446121991, -73300133084596)
(331498036727494507/21613201, -65074088586240778697297696/100479771449)
(8551101607, 380726514572396)
(15059910375, 581151524926316)
(15061168807, 581456090444396)
(572000021039/25, 300488965666985628/125)
(2039259052560927/121801, 41296165002969254598684/42508549)

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