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curve #5495

y2 = x3 + 442225
a-invariants
[0, 0, 0, 0, 442225]
c-invariants
[0, -382082400]
rank (lower bound)
≥ 3
torsion subgroup
ℤ/3ℤ
family
y2 = x3 + k (Mordell curves)
conductor (N)
15920100
discriminant (Δ)
-84483194670000
Faltings height
1.3512
naive height
39.5223
primes of bad reduction
2, 3, 5, 7, 19
regulator
541.66284309937481453903836858269729480394857
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 #5172: https://elliptic-rank.icarm.cloud/curve/5172 The source model is y^2 = x^3 - 11940075. Applying the standard rational 3-isogeny and scaling by u = 3 gives y^2 = x^3 + 442225. The three submitted points are exact transported points. PARI/GP 2.17.4 returned rank bounds [3,3], torsion Z/3Z, conductor 15920100, and minimal discriminant -84483194670000. 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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