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curve #3401

y2 + xy + y = x3 − x2 − 7274227818972119x + 238796779026136837315439
a-invariants
[1, -1, 1, -7274227818972119, 238796779026136837315439]
rank (lower bound)
≥ 2
torsion subgroup
ℤ/9ℤ
conductor (N)
8825955642
discriminant (Δ)
-2205063300352431019556068635503699951616
Faltings height
7.4693
naive height
121.1829
primes of bad reduction
2, 3, 7, 29, 271, 2971
regulator
223.316026026613326353416951300563404264975
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/9ℤ: y^2 + (1-c)xy - by = x^3 - bx^2 with c=t^2(t-1), b=c(t^2-t+1), at t = 1/29; converted to the global minimal model. The 2 witness points were found with PARI/GP ellrank. Conductor 8825955642, torsion ℤ/9ℤ.

last edited by David Renshaw at · history

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