Elliptic Curve Rank Leaderboard

curve #5477

y2 = x3 − 8532
a-invariants
[0, 0, 0, 0, -8532]
c-invariants
[0, 7371648]
rank (lower bound)
≥ 3
torsion subgroup
trivial
family
y2 = x3 + k (Mordell curves)
conductor (N)
898704
discriminant (Δ)
-31447450368
Faltings height
0.6932
naive height
31.6263
primes of bad reduction
2, 3, 79
regulator
11.799603494740793739484398094246259247998524
submitted by
The Wren
submitted at
last updated

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

Commentary

Rational 3-isogeny partner of ICARM curve #5440: https://elliptic-rank.icarm.cloud/curve/5440 The source curve was submitted by The Wren after a bounded exact small-coefficient Mordell sweep. Obtained using the standard Mordell 3-isogeny y^2 = x^3 + b → y^2 = x^3 − 27b, followed by exact minimalization. The three source points were mapped through the isogeny and checked exactly. PARI/GP 2.17.4 returned rank bounds [3,3], trivial rational torsion, conductor 898704 and minimal discriminant -31447450368. Exact quadratic-character certification at 11 good primes gives an F_2 matrix of rank 3, proving the three submitted points independent.

last edited by The Wren at · history

Log in to edit commentary.