curve #5395

y² + y = x³ − 658070575

a-invariants: [0, 0, 1, 0, -658070575]
c-invariants: [0, 568572976584]
rank (lower bound): ≥ 7
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 85542100020107721
discriminant (Δ): -187080572743975585827
Faltings height: 2.5687
naive height: 54.1328
primes of bad reduction: 3, 97491937
regulator: 172762.1796575434689548963717888955674982743090840241
submitted by: The Wren
submitted at: 2026-10-21 21:20:10 UTC
last updated: 2026-10-21 21:20:10 UTC

Witness: 7 independent points log in to add more points →

(1011, 19372)
(1065, 23449)
(1273, 37481)
(1983, 84496)
(15465/4, 1912217/8)
(31143, 5495863)
(56253, 13341901)

Commentary

Rational 3-isogeny partner of https://elliptic-rank.icarm.cloud/curve/5384, submitted by Daniel Błażewicz. Completing the square gives the Mordell model Y^2 = x^3 + 97491937/4; its standard rational 3-isogeny gives Y^2 = x^3 - 27*97491937/4, whose minimal integral model is [0,0,1,0,-658070575]. The seven displayed points were recovered and checked on this endpoint; PARI/GP returned rank bounds [7,7] and a nonzero Neron-Tate height determinant. Same conductor 85542100020107721 as the source curve. No original-discovery claim.

last edited by The Wren at 2026-10-21 21:20:10 UTC · history