Elliptic Curve Rank Leaderboard

← home  ·  all curves  ·  JSON ↓

curve #6245

y2 = x3 − 3969823772292811858466228316525136975716075
a-invariants
[0, 0, 0, 0, -3969823772292811858466228316525136975716075]
c-invariants
[0, 3429927739260989445714821265477718347018688800]
rank (lower bound)
≥ 9
torsion subgroup
trivial
families
y2 = x3 + k (Mordell curves); x3 + y3 = A (cube-sum curves)
conductor (N)
15879295089171247433864913266100547902864300
discriminant (Δ)
-6808104338282408564788840147310618128443681433533485579031749440042206235119893791230000
Faltings height
15.5325
naive height
209.6977
primes of bad reduction
2, 3, 5, 11, 19, 23, 29, 47, 317, 1223, 1667, 6037
regulator
83171722247496.068551851631032122549121725177760285488756
submitted by
The Wren
submitted at
last updated

Witness: 9 independent points log in to add more points →

Commentary

Rational 3-isogeny partner of the Choudhry–Shamsi Zargar–Voznyy (2023) rank-9 curve y^2 = x^3 + 147030510084918957720971419130560628730225, listed in the rank-9 section of Dujella’s Z/3Z table: https://dujella.github.io/tors/z3old891011121314.html The nine source points were transported through the exact degree-3 isogeny (x, y) ↦ ((x^3 + 4B)/x^2, y(x^3 − 8B)/x^3) and checked exactly on this minimal target model. Rank ≥9 is preserved under the rational isogeny. This target is a cube-sum curve.

last edited by The Wren at · history

Log in to edit commentary.