curve #4025

y² = x³ − 4711662178043464092028054346543860952537020107x + 124460131816261012046311906045455713523225457223448729419834808943306

a-invariants: [0, 0, 0, -4711662178043464092028054346543860952537020107, 124460131816261012046311906045455713523225457223448729419834808943306]
c-invariants: [226159784546086276417346608634105325721776965136, -107533553889249514408013486823273736484066795041059702218737274927016384]
rank (lower bound): ≥ 12
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 205992707064356143394663394290058360729592715459384018640
discriminant (Δ): 2437250313452494166092870688810053988631522904955999670839457671198416699610549548501976463572139488608100992795365123991689936144000000
Faltings height: 24.9741
naive height: 327.1127
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 29, 41, 53, 83, 101, 113, 163, 263, 313, 379, 523, 683, 1009, 2347, 13187, 30643, 1218199
regulator: 5109685600364.6281775129699784563257374973941449587655740498845
submitted by: dujella
submitted at: 2026-10-05 06:59:13 UTC
last updated: 2026-10-05 06:59:13 UTC

Witness: 12 independent points log in to add more points →

(6881879378314290760697, 9610461417551363095273928304683760)
(39139972711998386878937, 76113552417092114840678092730400)
(31456376828535335175137, 2715604965382414384198603255532400)
(42525133885662171699242, 998982819205576345498682487593430)
(108478624288484753812537609/9, 1129819916404683650081232980539800463520/27)
(39131331902619802203827, 82480756113675078494833306063710)
(4365423023221103348985, 10196809539063099929716219364034256)
(-35483241968455022684733, 15715267543929923566042939131815330)
(364461201149282230946533/9, 6990835980786855945584794195338100/27)
(29492187025766238148662, 3339894060967124719307926367190500)
(86670566714014790569592469/1369, 452818454518942895771014171936492407020/50653)
(150173757630386266592597747/1681, 1406599705973138071938844270272076723950/68921)

Commentary

Induced by the rational Diophantine triple {−39452128128/28866148597, 2685099/251184725, −5975179056/249448225}. Construction described in A. Dujella and J. C. Peral, High rank elliptic curves induced by rational Diophantine triples, Glas. Mat. Ser. III 55 (2020), 237-252.

last edited by dujella at 2026-10-05 06:59:14 UTC · history