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curve #5878

y2 + y = x3 − x2 − 1684944200x + 51357858049262
a-invariants
[0, -1, 1, -1684944200, 51357858049262]
c-invariants
[80877321616, -44372704090632920]
rank (lower bound)
≥ 13
torsion subgroup
trivial
conductor (N)
277759817061511866219351665481
discriminant (Δ)
-833279451184535598658054996443
Faltings height
4.4325
naive height
76.6628
primes of bad reduction
3, 4793, 19317046878191241826229339
regulator
41438840888.40117611165715061838552223574029150088589268732134193
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, 31st 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 277759817061511866219351665481. The construction author and search method are not identified in the source row.

last edited by The Wren at · history

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