Elliptic Curve Rank Leaderboard

← home  ·  all curves  ·  JSON ↓

curve #6453

y2 = x3 + x2 − 95103377488059225107308383633x + 10772663462220623101150623049774237487914863
a-invariants
[0, 1, 0, -95103377488059225107308383633, 10772663462220623101150623049774237487914863]
c-invariants
[4564962119426842805150802414400, -9307581231358645749166854876061772094372928000]
rank (lower bound)
≥ 11
torsion subgroup
ℤ/2ℤ × ℤ/2ℤ
conductor (N)
190274465488636094225424596624908315200
discriminant (Δ)
4917607384809166461910357876710211747881908179575551021902299207823486030723641600000000
Faltings height
15.5841
naive height
211.7879
primes of bad reduction
2, 3, 5, 7, 11, 13, 17, 37, 53, 71, 73, 89, 97, 139, 151, 2221, 6263, 7109, 12791
regulator
36268786223.5449256167372560541796007521598109587942793326072
submitted by
The Wren
submitted at
last updated

Witness: 11 independent points log in to add more points →

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=-71/306. 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 Rank bounds [11,11]. The eleven 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 190274465488636094225424596624908315200.

last edited by The Wren at · history

Log in to edit commentary.