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curve #5489

y2 = x3 + 182329
a-invariants
[0, 0, 0, 0, 182329]
c-invariants
[0, -157532256]
rank (lower bound)
≥ 3
torsion subgroup
ℤ/3ℤ
family
y2 = x3 + k (Mordell curves)
conductor (N)
19691532
discriminant (Δ)
-14361349352112
Faltings height
1.2035
naive height
37.7503
primes of bad reduction
2, 3, 7, 61
regulator
306.33552459131951968651330181861590996962514
submitted by
The Wren
submitted at
last updated

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

Commentary

Rational 3-isogeny partner of hdeping’s ICARM curve #5166: https://elliptic-rank.icarm.cloud/curve/5166 For the source model y^2 = x^3 - 4922883, the standard 3-isogenous Mordell model is y^2 = x^3 + 132917841. Rational scaling by u = 3 gives the minimal integral model y^2 = x^3 + 182329. The three submitted points are exact images under this isogeny and scaling. PARI/GP 2.17.4 returned rank bounds [3,3], rational torsion Z/3Z, conductor 19691532 and minimal discriminant -14361349352112. Exact quadratic-character certification at 12 good primes gives an F_2 matrix of rank 3, proving the three submitted points independent modulo torsion.

last edited by The Wren at · history

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