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curve #5493

y2 = x3 + 260100
a-invariants
[0, 0, 0, 0, 260100]
c-invariants
[0, -224726400]
rank (lower bound)
≥ 3
torsion subgroup
ℤ/3ℤ
family
y2 = x3 + k (Mordell curves)
conductor (N)
7022700
discriminant (Δ)
-29225668320000
Faltings height
1.2627
naive height
38.4608
primes of bad reduction
2, 3, 5, 17
regulator
6234.4967690131582745846969658467835553102560
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 #5170: https://elliptic-rank.icarm.cloud/curve/5170 The source model is y^2 = x^3 - 7022700. Applying the standard rational 3-isogeny and scaling by u = 3 gives y^2 = x^3 + 260100. The three submitted points are exact transported points. PARI/GP 2.17.4 returned rank bounds [3,3], torsion Z/3Z, conductor 7022700, and minimal discriminant -29225668320000. Exact quadratic-character certification at 11 good primes gives an F2 matrix of rank 3, proving the three submitted points independent modulo torsion.

last edited by The Wren at · history

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