Elliptic Curve Rank Leaderboard

curve #4993

y2 = x3 − 78918077x
a-invariants
[0, 0, 0, -78918077, 0]
c-invariants
[3788067696, 0]
rank (lower bound)
≥ 5
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
4067306368899872
discriminant (Δ)
31456431725936189371042112
Faltings height
3.5820
naive height
66.1654
primes of bad reduction
2, 7, 19, 29, 37, 79
regulator
2468.24341508875373140039512738148290952776233590
submitted by
The Wren
submitted at
last updated

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

Commentary

Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (14,28,32,34), 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. Five rational points checked exactly; PARI/GP returned rank bounds [5,5]. Rational torsion C2.

last edited by The Wren at · history

Log in to edit commentary.