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curve #3368

y2 + xy = x3 − 705036696x + 7814059186752
a-invariants
[1, 0, 0, -705036696, 7814059186752]
rank (lower bound)
≥ 2
torsion subgroup
ℤ/7ℤ
conductor (N)
9096906
discriminant (Δ)
-3948839685064974266724777984
Faltings height
4.0350
naive height
72.8971
primes of bad reduction
2, 3, 7, 13, 16661
regulator
8.43938008405163067603977566220661834158270
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/7ℤ: y^2 + (1-c)xy - by = x^3 - bx^2 with b=t^3-t^2, c=t^2-t, at t = 8/21; converted to the global minimal model. The 2 witness points were found with PARI/GP ellrank. Conductor 9096906, torsion ℤ/7ℤ.

last edited by David Renshaw at · history

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