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curve #6086

y2 = x3 − 3171398829493291218884119644426987x + 68545556755905241935851514559760537661771922781034
a-invariants
[0, 0, 0, -3171398829493291218884119644426987, 68545556755905241935851514559760537661771922781034]
c-invariants
[152227143815677978506437742932495376, -59223361037102129032575708579633104539770941282813376]
rank (lower bound)
≥ 13
torsion subgroup
ℤ/2ℤ × ℤ/2ℤ
conductor (N)
92611563353346759675602332566666653471281680 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 13
discriminant (Δ)
11671781451031797846610595194896594637987255180957280851880721496502288073746867680324667590416000000 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 13
Faltings height
18.0660 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 13
naive height
243.0320 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 13
primes of bad reduction
2, 3, 5, 7, 11, 13, 73, 79, 97, 101, 103, 139, 181, 421, 653, 787, 997, 2411, 6701, 35977
regulator
159117457690104.3607529419577446782663739375717093178538101180977
submitted by
The Wren
submitted at
last updated

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

Commentary

Original specialization/search by 0xArion (2026), public Yukon elliptic-rank challenge submission e4015be6-ebb5-475f-b505-f1b867f7cc35. Source: https://raw.githubusercontent.com/Layr-Labs/elliptic-rank-challenge-public/c1890e67b75e1de012b04c7add6c860ec2ba495e/submission/board/2x2-13-p724-q10981.ec . Specialization T=724/10981 of the rank-five X400a family posted by wgxli with curve#4252: y^2=x(x+A)(x+B), A=q(121q-99p)(26p-23q)(75p-44q), B=p(21q-74p)(25p-36q)(p+77q). The thirteen supplied points have been checked exactly on the minimal model and certified independent modulo torsion by an exact rank-13 F_7 reduction matrix at thirteen good primes.

last edited by The Wren at · history

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