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curve #3759

y2 + y = x3 + x2 − 73844607x + 244220728125
a-invariants
[0, 1, 1, -73844607, 244220728125]
rank (lower bound)
≥ 3
torsion subgroup
ℤ/3ℤ
conductor (N)
14526811
discriminant (Δ)
-14526811 ☆ record for ℤ/3ℤ torsion, rank ≥ 3
Faltings height
2.6275
naive height
65.9660
primes of bad reduction
13, 19, 103, 571
regulator
482.60662064579865213684679244799978049325979
submitted by
jesper-petersen
submitted at
last updated

Witness: 3 independent points log in to add more points →

Commentary

Found by an exhaustive discriminant sweep of the integral Tate X_1(3) family y^2 + a*x*y + b*y = x^3, for which Delta = b^3*(a^3 - 27*b), below the previous rank-3 discriminant threshold. Parameters a=244, b=-1 give Delta=-14526811. PARI/GP 2.17.4 gives rank bounds [3,3] and torsion invariants [3]; the three supplied rational points lie on the global minimal model and are independent.

last edited by jesper-petersen at · history

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