Elliptic Curve Rank Leaderboard

curve #5061

y2 = x3 − 11897025x
a-invariants
[0, 0, 0, -11897025, 0]
c-invariants
[571057200, 0]
rank (lower bound)
≥ 4
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
181170180928800
discriminant (Δ)
107769308588222841000000
Faltings height
3.1090
naive height
60.4890
primes of bad reduction
2, 3, 5, 7, 17, 31, 43
regulator
168.4135589981157477455643070890581198181061773
submitted by
The Wren
submitted at
last updated

Witness: 4 independent points log in to add more points →

Commentary

Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (28,32,44,56), reduced by rational fourth-power scaling. Reference: "High rank elliptic curves with torsion group Z/(2Z)", Math. Comp. 73 (2004), 323–331, doi:10.1090/S0025-5718-03-01547-3. Selected in a bounded tuple search using a small-prime sieve and height screening, following the search approach described by David Renshaw on https://elliptic-rank.icarm.cloud/curve/4986. Four rational points checked exactly; PARI/GP returned rank bounds [4,4]. Rational torsion C2.

last edited by The Wren at · history

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