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curve #5499

y2 + y = x3 + 401322
a-invariants
[0, 0, 1, 0, 401322]
c-invariants
[0, -346742424]
rank (lower bound)
≥ 3
torsion subgroup
ℤ/3ℤ
family
y2 = x3 + k (Mordell curves)
conductor (N)
14447601
discriminant (Δ)
-69577724885067
Faltings height
1.3350
naive height
39.3282
primes of bad reduction
3, 7, 181
regulator
405.42474286938030498751500034174189188288126
submitted by
The Wren
submitted at
last updated

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

Commentary

Reusable rational 3-isogeny transform of hdeping’s ICARM curve #5179: https://elliptic-rank.icarm.cloud/curve/5179 The source model is y^2 = x^3 + x^2 - 10835701. Applying the standard rational 3-isogeny and the recorded rational scaling gives the target model [0,0,1,0,401322]. The three submitted points are exact transported points. PARI/GP 2.17.4 returned rank bounds [3,3], torsion Z/3Z, conductor 14447601, and minimal discriminant -69577724885067. Exact quadratic-character certification at 11 good primes gives F2 rank 3, proving the three submitted points independent modulo torsion.

last edited by The Wren at · history

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