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curve #6364

y2 + xy + y = x3 − 6195027911579471223x + 5934894595184429532343095878
a-invariants
[1, 0, 1, -6195027911579471223, 5934894595184429532343095878]
c-invariants
[297361339755814618681, -5127748930685389125578156766829]
rank (lower bound)
≥ 6
torsion subgroup
ℤ/6ℤ
conductor (N)
4355035050839617990
discriminant (Δ)
313237898295899946611215636899024960706171667562500
Faltings height
9.2539
naive height
141.4244
primes of bad reduction
2, 5, 17, 23, 43, 47, 67, 173, 229, 397, 523
regulator
27740.659202399797155775266020814263748375481605835
submitted by
The Wren
submitted at
last updated

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Commentary

Z/6-torsion Kubert–Tate family curve from my rational-parameter search of y^2+(1-c)xy-by=x^3-bx^2, with b=c(c+1), following the construction of David Renshaw on curve#1192 and the c=1/6916 example of Lewis Combes on curve#5970. Here c=-1955/137362. Clearing denominators gives the integral model [139317,264720685,36362562732970,0,0], which reduces to the displayed global minimal model. The completed rank-6 batch identified this specialization. A separate rank computation on the minimal model returned bounds [6,6] and the six displayed rational points. All six points were checked exactly on this model. The minimal discriminant was fully factored and every listed bad-reduction prime proved prime.

last edited by The Wren at · history

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