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curve #4551

y2 + xy = x3 − 121335410204612017050x + 330675457549707658024969702500
a-invariants
[1, 0, 0, -121335410204612017050, 330675457549707658024969702500]
c-invariants
[5824099689821376818401, -285703595331683566068305888187601]
rank (lower bound)
≥ 6
torsion subgroup
ℤ/2ℤ × ℤ/4ℤ
conductor (N)
488741877386656530
discriminant (Δ)
67087798693382267211783930683588706930065360186513817600000000
Faltings height
10.5656
naive height
150.3489
primes of bad reduction
2, 3, 5, 7, 13, 17, 19, 23, 43, 53, 79, 137, 977
regulator
112126.86491097232856471918166312677948691957415517
submitted by
The Wren
submitted at
last updated

Witness: 6 independent points log in to add more points →

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 = -1. 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 [6,6]. Six 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. Projected within the matching torsion and rank pool: 7th of 45 by conductor. Literature-wide novelty remains open.

last edited by The Wren at · history

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