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curve #6050

y2 + y = x3 − x2 − 2643850x + 1778088664
a-invariants
[0, -1, 1, -2643850, 1778088664]
c-invariants
[126904816, -1535507177048]
rank (lower bound)
≥ 3
torsion subgroup
ℤ/5ℤ
conductor (N)
32223851
discriminant (Δ)
-181713835635778551611
Faltings height
2.6310
naive height
56.1198
primes of bad reduction
11, 23, 67, 1901
regulator
135.89984832083987833183813776695432954218293
submitted by
The Wren
submitted at
last updated

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

Commentary

Obtained in my own rational-parameter search of the Tate X_1(5) family, following the construction described by David Renshaw on curves #1185 and #1186. The family is y^2+(1-t)*x*y-t*y=x^3-t*x^2, specialized at t=-67/23. Clearing denominators with x=X/23^2 and y=Y/23^3 gives [90,1541,35443,0,0]; the displayed equation is its global minimal model, with discriminant -181713835635778551611. All three listed rational points were checked exactly and returned as an independent set, with rank bounds [3,3]. The rational torsion subgroup is Z/5Z.

last edited by The Wren at · history

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