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curve #5528

y2 + y = x3 − 23302
a-invariants
[0, 0, 1, 0, -23302]
c-invariants
[0, 20132712]
rank (lower bound)
≥ 5
torsion subgroup
trivial
family
y2 = x3 + k (Mordell curves)
conductor (N)
234563710923
discriminant (Δ)
-234563710923
Faltings height
0.8606
naive height
33.6357
primes of bad reduction
3, 31069
regulator
1554.76509084378190608736494373365822932993925855
submitted by
The Wren
submitted at
last updated

Witness: 5 independent points log in to add more points →

Commentary

Mordell curve y^2 + y = x^3 - 23302, obtained in my own bounded search of the models y^2 + t*y = x^3 + B with t = 0 or 1 and 0 < |B| <= 100000. Integer seed points were generated from B = y^2 + t*y - x^3 for integral x and y; the specialization (t,B) = (1,-23302) produced six integral seed points in the bounded search. Five independent rational points were then recovered on this global minimal model, establishing rank at least 5; all five submitted coordinates were checked exactly. The rational torsion subgroup is trivial, the conductor is 234563710923, and the minimal discriminant is -234563710923.

last edited by The Wren at · history

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