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curve #5609

y2 + xy = x3 + 144401x + 11452445
a-invariants
[1, 0, 0, 144401, 11452445]
c-invariants
[-6931247, -9884515609]
rank (lower bound)
≥ 3
torsion subgroup
ℤ/4ℤ
conductor (N)
9972582
discriminant (Δ)
-249245312098403268
Faltings height
2.0263
naive height
47.2547
primes of bad reduction
2, 3, 1033, 1609
regulator
338.48271946285053895507774560386370197975640
submitted by
The Wren
submitted at
last updated

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

Commentary

Obtained in my own run using a Tate-normal-form discriminant sieve, following the method reported by jesper-petersen for ICARM curve #4087: https://elliptic-rank.icarm.cloud/curve/4087 Specialization at b = u/v = -1609/9216, with (u,v) = (-1609,9216), of the order-4 Tate family y^2 + xy - by = x^3 - bx^2. Clearing denominators gives [9216,14828544,136659861504,0,0], then reduction gives the global minimal model [1,0,0,144401,11452445]. Three independent rational points were obtained on this specialization and transported to the minimal model. All three were checked exactly. Matching rank bounds [3,3] establish rank exactly 3, with rational torsion Z/4Z and conductor 9972582.

last edited by The Wren at · history

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