curve #6408

y² + xy = x³ − x² − 103576909948556253237324924x + 405718970840835891577109266708784169980

a-invariants: [1, -1, 0, -103576909948556253237324924, 405718970840835891577109266708784169980]
c-invariants: [4971691677530700155391596361, -350541190806459837710073518285690260679109]
rank (lower bound): ≥ 20
torsion subgroup: trivial
conductor (N): 1589246951838586754060051898405424987810548995592314831412812892810
discriminant (Δ): 5640679640039493476923441396881584591242496670615148898285913571770114382500
Faltings height: 13.6109
naive height: 191.3207
primes of bad reduction: 2, 3, 5, 7, 73, 1021, 6197, 5461610682851183182391913747241634138527055801874995687
regulator: 11547669250490014184.8141168568029417263967520227556077629682758985039496312154
submitted by: apkorte
submitted at: 2026-11-02 05:33:16 UTC
last updated: 2026-11-02 05:33:16 UTC

(5916986275306, 117491346585524572)
(3047845895431, -10878653221948953053)
(52328527811254/9, -6067674967880475806/27)
(5647925962841, 942241593161039727)
(5958116631286, -322120448065024298)
(6092033244676, -904339342486908458)
(1497575739556, 15936227349420612622)
(340994429686, 19246804015708774102)
(27963851888806, -139199148170308423628)
(41894384813086, 263812254688333647502)
(5489736903181, 1598229661729501372)
(5811018533095, -240277180390684490)
(5518486194611, -1479695425847381598)
(-6288535817780, -28432049835628946630)
(5202255725164, -2770645465219529678)
(5924208810626, -158880289197621758)
(5817915013681, -207089367070267553)
(5613975457546, -1083901078061236838)
(6266273672086, 1652380859486856502)
(6035890797781, -662945173309931228)

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