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curve #1778

y2 + xy = x3 − 18262097056293794050462967800x + 947221615382521776843113311413294620840000
a-invariants
[1, 0, 0, -18262097056293794050462967800, 947221615382521776843113311413294620840000]
rank (lower bound)
≥ 3
torsion subgroup
ℤ/2ℤ × ℤ/8ℤ
conductor (N)
486370782457448070
discriminant (Δ)
2188258744343393327073128208815979236032677046635246478348390767774386708505600000000
Faltings height
15.0491
naive height
206.8375
primes of bad reduction
2, 3, 5, 7, 13, 17, 19, 41, 61, 191, 353, 3271
regulator
1821.7809156640199043787820072949472700491756
submitted by
hdeping
submitted at
later contributions
  • rank ≥ 2 → ≥ 3 · hdeping ·

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

Commentary

Specialization t=91/61 of the universal torsion Z/2xZ/8 family y^2=x(x+16t^4)(x+(t^2-1)^4).

last edited by hdeping at · history

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