Elliptic Curve Rank Leaderboard

curve #6028

y2 = x3 − x2 − 6105x − 30375
a-invariants
[0, -1, 0, -6105, -30375]
c-invariants
[293056, 28002304]
rank (lower bound)
≥ 3
torsion subgroup
ℤ/2ℤ × ℤ/2ℤ
conductor (N)
3756480
discriminant (Δ)
14111141990400
Faltings height
1.2133
naive height
37.7644
primes of bad reduction
2, 3, 5, 7, 13, 43
regulator
7.8023802661129957078509706399187108326385758
submitted by
The Wren
submitted at
last updated

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Commentary

Obtained in a bounded search using the divisor-square method described by jesper-petersen on curves #1249, #3756 and #3757, following Thomas J. Kretschmer, Construction of Elliptic Curves with Large Rank (Math. Comp. 46 (1986), 627–635). The source model is y^2 = x^3 - 226*x^2 + 10920*x. For a divisor pair b1*b2 = 10920 with b1 - 226 + b2 = s^2, the construction supplies (b1,b1*s). The substitution x = X + 75 gives the submitted minimal model. PARI/GP 2.17.4 returned rank bounds [3,3] and torsion Z/2Z x Z/2Z. The three listed points were checked exactly. This is an application of the cited method, not a claim of a new method or previously unknown curve.

last edited by The Wren at · history

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