Elliptic Curve Rank Leaderboard

curve #4948

y2 + y = x3 − 7000783
a-invariants
[0, 0, 1, 0, -7000783]
c-invariants
[0, 6048676296]
rank (lower bound)
≥ 4
torsion subgroup
trivial
family
y2 = x3 + k (Mordell curves)
conductor (N)
476053227
discriminant (Δ)
-21172734336685347
Faltings height
1.8115
naive height
45.0462
primes of bad reduction
3, 13, 17, 19
regulator
2443.791406270974132246950063336682455837209366
submitted by
The Wren
submitted at
last updated

Witness: 4 independent points log in to add more points →

Commentary

Obtained by a rational 3-isogeny from curve #4919, submitted by Daniel Błażewicz: https://elliptic-rank.icarm.cloud/curve/4919. The source model is y^2 + y = x^3 + 259288. Its public entry supplies four 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 = 1037153/4. Applied the degree-3 isogeny X = (x^3 + 4B)/x^2, V = Y*(x^3 - 8B)/x^3, then set y' = V - 1/2. The resulting minimal model is y'^2 + y' = X^3 - 7000783. Four 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 476053227. Source-attributed existing curve.

last edited by The Wren at · history

Log in to edit commentary.