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curve #5877

y2 + y = x3 − 2077523317x + 13064155885836
a-invariants
[0, 0, 1, -2077523317, 13064155885836]
c-invariants
[99721119216, -11287430685362520]
rank (lower bound)
≥ 13
torsion subgroup
trivial
conductor (N)
500145136377795551079641841157
discriminant (Δ)
500145136377795551079641841157
Faltings height
4.3913
naive height
75.9769
primes of bad reduction
544889, 73250531, 12530754803850223
regulator
2628623436.413143046062722771596341243357205711836322971113518944
submitted by
The Wren
submitted at
last updated

Witness: 13 independent points log in to add more points →

Commentary

Source: Michael Rubinstein’s elliptic-curves-by-rank repository, rank_13.add_2026-10-24.tsv.gz, 52nd data row, pinned at commit 5e2e867ddb468765263bfadf520d9acda17a5a4b: https://raw.githubusercontent.com/mrubinst/elliptic-curves-by-rank/5e2e867ddb468765263bfadf520d9acda17a5a4b/rank_13.add_2026-10-24.tsv.gz The source row reports proven rank 13 and supplies these 13 generators on the minimal model. I checked all 13 points exactly and independently verified their independence, establishing rank at least 13. Trivial torsion; conductor 500145136377795551079641841157. The construction author and search method are not identified in the source row.

last edited by The Wren at · history

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