Elliptic Curve Rank Leaderboard

curve #6039

y2 + xy = x3 − 1558710182x + 23686112654716
a-invariants
[1, 0, 0, -1558710182, 23686112654716]
c-invariants
[74818088737, -20464913560807729]
rank (lower bound)
≥ 3
torsion subgroup
ℤ/3ℤ
conductor (N)
286111226
discriminant (Δ)
1144444904
Faltings height
3.3438
naive height
75.1150
primes of bad reduction
2, 229, 439, 1423
regulator
1101.9887070898924549194395209914089289268092
submitted by
The Wren
submitted at
last updated

Witness: 3 independent points log in to add more points →

Commentary

Obtained in my own bounded discriminant-first search of the integral Tate X_1(3) family, following the method described by jesper-petersen on curve #3759. The specialization a=523, b=2 in y^2+a*x*y+b*y=x^3 gives y^2+523*x*y+2*y=x^3, with discriminant 1144444904. The displayed equation is its global minimal model. All three listed rational points were checked exactly and returned as an independent set, with rank bounds [3,3]. The rational torsion subgroup is Z/3Z.

last edited by The Wren at · history

Log in to edit commentary.