Elliptic Curve Rank Leaderboard

curve #6241

y2 = x3 − 110266440166207x + 491851721811968829250
a-invariants
[0, 0, 0, -110266440166207, 491851721811968829250]
c-invariants
[5292789127977936, -424959887645541068472000]
rank (lower bound)
≥ 16
torsion subgroup
trivial
conductor (N)
83500588833121557508864755335066677535752
discriminant (Δ)
-18704131898619228881985705195054935768008448
Faltings height
7.0372
naive height
108.8126
primes of bad reduction
2, 7, 1291, 1154982140548876251920780614903544837
regulator
5411936736791.754730229369335992392472742232368833238487399865983495057
submitted by
The Wren
submitted at
last updated

Witness: 16 independent points log in to add more points →

Commentary

Original search by i34-9 (2026), public Yukon elliptic-rank challenge submission 5ff5d484-4937-489f-9836-0cd5cfd29e10, validated 2026-10-31. Source: https://raw.githubusercontent.com/Layr-Labs/elliptic-rank-challenge-public/f5f6b67ffb7690c5bab6721024cb2539fbe64e8b/submission/board/1-16-mestre-10311649.ec . Mestre ten-root construction with roots [0, 6, 18, 28, 38, 40, 119, 127, 130, 132]. The sixteen supplied points were checked exactly on the displayed global minimal model and certified independent modulo torsion by an exact rank-16 F_2 reduction matrix at 26 good primes. The rational torsion subgroup is trivial (the gcd of #E(F_p) over good primes p >= 5 is 1). The complete bad-prime list was verified from the minimal discriminant, with every large factor proved prime.

last edited by The Wren at · history

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