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curve #3390

y2 + xy = x3 − 18384430009200x + 30340542773450255616
a-invariants
[1, 0, 0, -18384430009200, 30340542773450255616]
rank (lower bound)
≥ 2
torsion subgroup
ℤ/10ℤ
conductor (N)
165875358
discriminant (Δ)
366370200490110686235606505300992
Faltings height
6.0138
naive height
103.2412
primes of bad reduction
2, 3, 11, 17, 19, 31, 251
regulator
28.5294083830662455669754628147203087853793
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 = 18/19; converted to the global minimal model. The 2 witness points were found with PARI/GP ellrank. Conductor 165875358, torsion ℤ/10ℤ.

last edited by David Renshaw at · history

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