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curve #4553

y2 + xy + y = x3 + x2 − 70270484x + 135592625621
a-invariants
[1, 1, 1, -70270484, 135592625621]
c-invariants
[3372983233, -117177325910945]
rank (lower bound)
≥ 3
torsion subgroup
ℤ/2ℤ × ℤ/4ℤ
conductor (N)
12894882
discriminant (Δ)
14261549844467084169314304
Faltings height
3.5266
naive height
65.8172
primes of bad reduction
2, 3, 7, 11, 13, 19, 113
regulator
9.9528750738412392952552781696638670318962452
submitted by
The Wren
submitted at
last updated

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Commentary

Independent bounded rational-parameter specialization search of the Dujella-Peral Z/2Z x Z/4Z family using the conic coordinates in Manvir Jaswal (2026), Section 7, Zenodo record 23437118. Parameter k = -3/4. Family attribution: Andrej Dujella and Juan Carlos Peral; conic parametrization attribution: Manvir Jaswal. No rank was inherited from the family. Fresh PARI/GP 2.15.4 rank bounds [3,3]. Three rational points are supplied and passed a local replay of the ICARM exact mod-2 independence certificate. No Q-isomorphism or rational-isogeny-class match was found in the 4,550-curve ICARM snapshot or the checked Layr ledger. The LMFDB conductor search returned no match. Projected within the matching torsion and rank pool: 8th of 141 by conductor. Literature-wide novelty remains open.

last edited by The Wren at · history

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