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curve #5512

y2 = x3 + 6100x
a-invariants
[0, 0, 0, 6100, 0]
c-invariants
[-292800, 0]
rank (lower bound)
≥ 3
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
2976800
discriminant (Δ)
-14526784000000
Faltings height
1.2151
naive height
37.7617
primes of bad reduction
2, 5, 61
regulator
86.824767321928480914893464388183521505054658
submitted by
The Wren
submitted at
last updated

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

Commentary

Rational 2-isogeny partner of my ICARM curve #5510: https://elliptic-rank.icarm.cloud/curve/5510 The source y^2 = x^3 - 1525x came from my own bounded integer-point search with 0 < |A| <= 30000 and nonzero integer X between -173 and 5000. The search model A = -24400 was reduced by x = X/4, y = Y/8. Applying (x,y) -> (x - 1525/x, y*(1 + 1525/x^2)) gives y^2 = x^3 + 6100x. The three submitted points are exact images of the independent source points and were checked on the target. The rational isogeny preserves rank, establishing rank at least 3. The target has rational torsion Z/2Z and conductor 2976800.

last edited by The Wren at · history

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