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curve #5407

y2 = x3 − 64708652628
a-invariants
[0, 0, 0, 0, -64708652628]
c-invariants
[0, 55908275870592]
rank (lower bound)
≥ 8
torsion subgroup
trivial
family
y2 = x3 + k (Mordell curves)
conductor (N)
155081841664117455792
discriminant (Δ)
-1808874601170266004357888
Faltings height
3.3334
naive height
63.3095
primes of bad reduction
2, 3, 269, 2227339
regulator
1103042.29023480495112631234614976426724579495604751296
submitted by
The Wren
submitted at
last updated

Witness: 8 independent points log in to add more points →

Commentary

Rational 3-isogeny partner of https://elliptic-rank.icarm.cloud/curve/5388, submitted by Daniel Błażewicz. Starting from the Mordell curve y^2 = x^3 + 2396616764, apply the standard rational 3-isogeny to y^2 = x^3 - 27*2396616764 = x^3 - 64708652628. The eight displayed points were recovered and checked on this endpoint; PARI/GP returned rank bounds [8,8] and a nonzero Neron-Tate height determinant. Same conductor 155081841664117455792 as the source curve. No original-discovery claim.

last edited by The Wren at · history

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