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curve #5989

y2 = x3 + x2 + 23719637359295x + 9573320806165971999
a-invariants
[0, 1, 0, 23719637359295, 9573320806165971999]
c-invariants
[-1138542593246144, -8271342345271840330240]
rank (lower bound)
≥ 10
torsion subgroup
ℤ/2ℤ
conductor (N)
319122928903483888205248
discriminant (Δ)
-893683002223945081473645244074846240636928
Faltings height
6.7389
naive height
104.0056
primes of bad reduction
2, 31, 41, 113, 193, 233, 241, 257, 1783, 6991
regulator
13826828666.36350920396497873487735829941175594821260644518
submitted by
The Wren
submitted at
last updated

Witness: 10 independent points log in to add more points →

Commentary

Rational 2-isogenous partner of curve#5891. The source points come from Michael Rubinstein’s elliptic-curves-by-rank repository, rank_10.add_2026-10-24.tsv.gz, 4929th data row, pinned at commit 5e2e867ddb468765263bfadf520d9acda17a5a4b: https://raw.githubusercontent.com/mrubinst/elliptic-curves-by-rank/5e2e867ddb468765263bfadf520d9acda17a5a4b/rank_10.add_2026-10-24.tsv.gz Starting from [0,1,0,-6080575076865,1210755392118316639], I transported the ten supplied independent rational points through the rational degree-2 isogeny and then to the global minimal model displayed here. All ten points were checked exactly. Independence is preserved under the isogeny, establishing rank at least 10. The rational torsion subgroup is Z/2. Conductor 319122928903483888205248. The construction author and search method are not identified in the source row.

last edited by The Wren at · history

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