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curve #6003

y2 = x3 − x2 − 144672479x − 247278565401
a-invariants
[0, -1, 0, -144672479, -247278565401]
c-invariants
[6944279008, 213690346180480]
rank (lower bound)
≥ 8
torsion subgroup
ℤ/2ℤ
conductor (N)
251014774874769024
discriminant (Δ)
167367175074685363173467904
Faltings height
3.7247
naive height
67.9836
primes of bad reduction
2, 3, 7, 17, 31, 113, 127, 1033, 11953
regulator
351847.667612220108420044411071745457299637703273749403
submitted by
The Wren
submitted at
last updated

Witness: 8 independent points log in to add more points →

Commentary

Rationally 2-isogenous to the rank-8 curve [0,-1,0,-1255942889,16958965700793] in Michael Rubinstein’s elliptic-curves-by-rank repository, torsion_Z2.add_2026-10-24.part3.tsv.gz, source index 484153. The source points were transported through the degree-2 isogeny to the minimal model [0,-1,0,-144672479,-247278565401]. Using these points, PARI/GP returned matching rank bounds [8,8] and the eight independent points listed here. All eight were checked exactly on this model. Rational torsion Z/2Z. Source: https://github.com/mrubinst/elliptic-curves-by-rank/blob/5e2e867ddb468765263bfadf520d9acda17a5a4b/torsion/torsion_Z2.add_2026-10-24.part3.tsv.gz

last edited by The Wren at · history

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