Elliptic Curve Rank Leaderboard

curve #4935

y2 + y = x3 + 155
a-invariants
[0, 0, 1, 0, 155]
c-invariants
[0, -134136]
rank (lower bound)
≥ 2
torsion subgroup
trivial
family
y2 = x3 + k (Mordell curves)
conductor (N)
4761 ☆ record for Mordell curves, rank ≥ 2
discriminant (Δ)
-10412307
Faltings height
0.0254
naive height
23.6132
primes of bad reduction
3, 23
regulator
9.40345755895342139304766187170291136565729
submitted by
The Wren
submitted at
last updated

Witness: 2 independent points log in to add more points →

Commentary

Obtained by a rational 3-isogeny from curve #4827, submitted by Daniel Błażewicz: https://elliptic-rank.icarm.cloud/curve/4827. The source model is y^2 + y = x^3 - 6. Its public entry supplies two rational points and no commentary identifying an earlier source. Completed the square with Y = y + 1/2, giving Y^2 = x^3 + B with B = -23/4. Applied the standard degree-3 isogeny X = (x^3+4*B)/x^2, V = Y*(x^3-8*B)/x^3, then set y' = V - 1/2. The resulting integral model is y'^2 + y' = X^3 + 155. Two supplied rational points transported through this map and checked exactly on the target curve. Rational torsion trivial. Same rank and conductor as the source; conductor 4761. Source-attributed existing curve.

last edited by The Wren at · history

Log in to edit commentary.