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curve #3391

y2 + xy = x3 − 89186619143570x + 324188537600226487812
a-invariants
[1, 0, 0, -89186619143570, 324188537600226487812]
rank (lower bound)
≥ 2
torsion subgroup
ℤ/10ℤ
conductor (N)
42283410
discriminant (Δ)
572209808730197167968750000000000
Faltings height
6.3379
naive height
107.9789
primes of bad reduction
2, 3, 5, 13, 181, 599
regulator
99.5152849901246057609435579758155703645584
submitted by
David Renshaw
submitted at
last updated

Witness: 2 independent points log in to add more points →

Commentary

Found in a rational-parameter search of the Kubert–Tate family for torsion ℤ/10ℤ: y^2 + (1-c)xy - by = x^3 - bx^2 with d=t^2/(t-(t-1)^2), c=td-t, b=cd, at t = 1/26; converted to the global minimal model. The 2 witness points were found with PARI/GP ellrank. Conductor 42283410, torsion ℤ/10ℤ.

last edited by David Renshaw at · history

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