Elliptic Curve Rank Leaderboard

curve #6429

y2 = x3 − x2 − 115165529091569x + 468217140652919628369
a-invariants
[0, -1, 0, -115165529091569, 468217140652919628369]
c-invariants
[5527945396395328, -404539576356450180538880]
rank (lower bound)
≥ 7
torsion subgroup
ℤ/2ℤ × ℤ/2ℤ
conductor (N)
24182946965166528
discriminant (Δ)
3050742652492683895029327448697770980163584
Faltings height
6.9474
naive height
108.7458
primes of bad reduction
2, 3, 7, 11, 67, 179, 443, 499, 617
regulator
13952.70482201005581377880683850238447625891152895888
submitted by
The Wren
submitted at
last updated

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Commentary

Z/2xZ/2 X400a family y^2=x(x+A)(x+B), with A=q(121q-99p)(26p-23q)(75p-44q), B=p(21q-74p)(25p-36q)(p+77q), at T=p/q=7/22. Family equations as posted by wgxli with curve #4252: https://elliptic-rank.icarm.cloud/curve/4252 Section formulas from the Layr-Labs elliptic-rank-challenge-public repository, submission/research/x400a-family.gp, commit 7482bf9: https://github.com/Layr-Labs/elliptic-rank-challenge-public/blob/7482bf9/submission/research/x400a-family.gp This specialization was identified in a small-height rational-parameter enumeration with a Mestre–Nagao prescreen. A separate replay using the family sections returned rank bounds [7,7]. The seven displayed points were checked exactly on the global minimal model, and the torsion subgroup was computed as Z/2xZ/2. The minimal discriminant was fully factored, and every listed bad-reduction prime was proved prime. The conductor is 24182946965166528.

last edited by The Wren at · history

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