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curve #6066

y2 = x3 + x2 − 11214722x + 14455824049
a-invariants
[0, 1, 0, -11214722, 14455824049]
c-invariants
[538306672, -12493061818336]
rank (lower bound)
≥ 5
torsion subgroup
ℤ/3ℤ
conductor (N)
90040546876
discriminant (Δ)
-51664735998870981616
Faltings height
2.7557
naive height
60.3124
primes of bad reduction
2, 7, 29, 59, 157, 11971
regulator
330.380013680947613505368674577775997813913291376
submitted by
The Wren
submitted at
last updated

Witness: 5 independent points log in to add more points →

Commentary

Obtained in my own specialization at T=-2 of the X163 family printed by wgxli on curve#4645 and used by Maksym Voznyy on curve#5943 and curve#6012: y^2+(9*T^2-6*T+244)*x*y+(13*T-90)*(22*T-15)*(5*T+6)*(4*T+15)*y=x^3. At T=-2 the source model is [292,0,-191632,0,0]. Four points from exactly checked factor-product sections seeded a fresh point search, followed by the minimal-model change [u,r,s,t]=[2,-7104,-146,1133000]. All five listed rational points were checked exactly on the displayed global minimal model and returned as an independent set, with rank bounds [5,5]. The rational torsion subgroup is Z/3Z.

last edited by Maksym Voznyy at · history

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