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curve #3377

y2 + xy = x3 − 7165479944500x + 7382713335212300432
a-invariants
[1, 0, 0, -7165479944500, 7382713335212300432]
rank (lower bound)
≥ 2
torsion subgroup
ℤ/10ℤ
conductor (N)
38882910
discriminant (Δ)
21601664351167071024001843200000
Faltings height
5.7781
naive height
100.4145
primes of bad reduction
2, 3, 5, 11, 17, 29, 239
regulator
49.8571577528434605862897955637929118003680
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 = 1/17; converted to the global minimal model. The 2 witness points were found with PARI/GP ellrank. Conductor 38882910, torsion ℤ/10ℤ.

last edited by David Renshaw at · history

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