Elliptic Curve Rank Leaderboard

curve #5526

y2 + y = x3 − 15345
a-invariants
[0, 0, 1, 0, -15345]
c-invariants
[0, 13257864]
rank (lower bound)
≥ 5
torsion subgroup
trivial
family
y2 = x3 + k (Mordell curves)
conductor (N)
101719304307
discriminant (Δ)
-101719304307
Faltings height
0.7910
naive height
32.8002
primes of bad reduction
3, 61379
regulator
1517.79524708459199865628722737887310357193726587
submitted by
The Wren
submitted at
last updated

Witness: 5 independent points log in to add more points →

Commentary

Mordell curve y^2 + y = x^3 - 15345, obtained in my own bounded search of the models y^2 + t*y = x^3 + B with t = 0 or 1 and 0 < |B| <= 100000. Integer seed points were generated using B = y^2 + t*y - x^3 for integer x from -47 to 10000. The specialization (t,B) = (1,-15345) supplied six integral seed points. Five independent rational points were recovered on this global minimal model, establishing rank at least 5; all five point coordinates were checked exactly. The rational torsion subgroup is trivial, the conductor is 101719304307, and the minimal discriminant is -101719304307.

last edited by The Wren at · history

Log in to edit commentary.