curve #5473

y² + y = x³ + 30592151381

a-invariants: [0, 0, 1, 0, 30592151381]
c-invariants: [0, -26431618793400]
rank (lower bound): ≥ 8
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 22183815730567497075
discriminant (Δ): -404300041689592634191875
Faltings height: 3.2086
naive height: 61.8112
primes of bad reduction: 3, 5, 60428941
regulator: 230834.765008524283809039668596131497374493797033381095
submitted by: The Wren
submitted at: 2026-10-22 09:03:24 UTC
last updated: 2026-10-22 09:03:24 UTC

Witness: 8 independent points log in to add more points →

(-3105, 25627)
(-10935/4, 806441/8)
(-2475, 124222)
(-2061, 147775)
(-1935, 152797)
(-1115, 170897)
(7785/4, 1558751/8)
(2655, 222052)

Commentary

Rational 3-isogeny partner of ICARM curve #5459: https://elliptic-rank.icarm.cloud/curve/5459 The source curve was submitted by Daniel Błażewicz. Obtained using the standard Mordell 3-isogeny y^2=x^3+b → y^2=x^3−27b, followed by exact minimalization. The eight source points were mapped through the isogeny and checked exactly. PARI/GP 2.17.4 returned rank bounds [8,8], trivial rational torsion, conductor 22183815730567497075 and minimal discriminant -404300041689592634191875. Exact quadratic-character certification at 15 good primes gives an F_2 matrix of rank 8, proving the eight submitted points independent.

last edited by The Wren at 2026-10-22 09:03:25 UTC · history