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curve #6029

y2 + y = x3 + x2 − 1143247607x + 14878098909045
a-invariants
[0, 1, 1, -1143247607, 14878098909045]
c-invariants
[54875885152, -12855006712725976]
rank (lower bound)
≥ 3
torsion subgroup
ℤ/3ℤ
conductor (N)
113379931
discriminant (Δ)
-113379931
Faltings height
3.2537
naive height
74.1850
primes of bad reduction
7, 79, 421, 487
regulator
791.70202612973507387684938898250492309596529
submitted by
The Wren
submitted at
last updated

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Commentary

Obtained in a bounded discriminant-first search of the integral Tate X_1(3) family, following the method described by jesper-petersen on curve #3759. The source model is y^2 + 484*x*y - y = x^3, with discriminant -113379931. Candidates were selected using finite-field scores, then checked on their global minimal models with PARI/GP 2.17.4. For this curve PARI returned rank bounds [3,3] and torsion Z/3Z; the three listed points were checked exactly. This applies the cited search method, Model order [a1,a2,a3,a4,a6]; y²+y=x³+x²−1143247607x+14878098909045.

last edited by The Wren at · history

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