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curve #4159
y2 + xy = x3 − x2 − 999511783603045092x + 383789404549981061806962816
- a-invariants
[1, -1, 0, -999511783603045092, 383789404549981061806962816]- c-invariants
[47976565612946164425, -331594045315289092142958133125]- rank (lower bound)
- ≥ 9
- torsion subgroup
- ℤ/2ℤ × ℤ/2ℤ
- conductor (N)
17092350793816085358450 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 9- discriminant (Δ)
275167648036995038807245573458061778333179339730250000- Faltings height
- 9.1316
- naive height
- 135.9517
- primes of bad reduction
2, 3, 5, 11, 23, 31, 113, 193, 239, 251, 487, 691- regulator
700968.51094455477990935520094172367480456811744453844418- submitted by
- NDElkies
- submitted at
- last updated
(-573835116, 27720100584708)(-863873007, 24547376095059)(545163204, 957043197048)(683304009, 4455735365283)(1211013444, 30811458290628)(529777284, 1720247354808)(489921204, 3420228735048)(-360870231, 26410184000628)(1380840465, -40454364625764)
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