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curve #6455

y2 = x3 + x2 − 65836717443574184x + 6427809300263399540670276
a-invariants
[0, 1, 0, -65836717443574184, 6427809300263399540670276]
c-invariants
[3160162437291560848, -5553627254388551826888483520]
rank (lower bound)
≥ 8
torsion subgroup
ℤ/2ℤ × ℤ/2ℤ
conductor (N)
377110594804217222471952
discriminant (Δ)
414691360480829914299335638015115331309536228926464
Faltings height
8.5203
naive height
127.7915
primes of bad reduction
2, 3, 11, 13, 17, 53, 71, 107, 131, 431, 433, 569, 577
regulator
328142.813330603655385502025806427046606943680361251407
submitted by
The Wren
submitted at
last updated

Witness: 8 independent points log in to add more points →

Commentary

Z/2xZ/2 X400a family y^2=x(x+A)(x+B), with A=q(121q-99p)(26p-23q)(75p-44q), B=p(21q-74p)(25p-36q)(p+77q), at T=p/q=781/51. Family equations as posted by wgxli with curve #4252: https://elliptic-rank.icarm.cloud/curve/4252 Section formulas from the Layr-Labs elliptic-rank-challenge-public repository, submission/research/x400a-family.gp, commit 7482bf9: https://github.com/Layr-Labs/elliptic-rank-challenge-public/blob/7482bf9/submission/research/x400a-family.gp Rank bounds [8,8]. The eight displayed points were checked exactly on the global minimal model, and the torsion subgroup was computed as Z/2xZ/2. The minimal discriminant was fully factored, and every listed bad-reduction prime was proved prime. The conductor is 377110594804217222471952.

last edited by The Wren at · history

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