Elliptic Curve Rank Leaderboard

curve #6427

y2 = x3 − 57774924656503675x + 5297411913653234638448250
a-invariants
[0, 0, 0, -57774924656503675, 5297411913653234638448250]
c-invariants
[2773196383512176400, -4576963893396394727619288000]
rank (lower bound)
≥ 8
torsion subgroup
ℤ/2ℤ × ℤ/2ℤ
conductor (N)
42313351568007232235600
discriminant (Δ)
219326415812428062112693530735486892303651600000000
Faltings height
8.4769
naive height
127.3996
primes of bad reduction
2, 5, 7, 11, 19, 61, 101, 131, 173, 239, 1259, 1721
regulator
1001929.16120505950258709701878429514486696860208770399
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=19/61. 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 [8,8]. The eight 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 42313351568007232235600.

last edited by The Wren at · history

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