Elliptic Curve Rank Leaderboard

← home  ·  all curves  ·  JSON ↓

curve #5698

y2 = x3 − 944292379418972x
a-invariants
[0, 0, 0, -944292379418972, 0]
c-invariants
[45326034212110656, 0]
rank (lower bound)
≥ 10
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
1783376195657487548808627073568 ☆ record for quartic twists, rank ≥ 10
discriminant (Δ)
53888913638290018498380350346329050897245827072
Faltings height
7.6564
naive height
115.0580
primes of bad reduction
2, 19, 157, 197, 313, 769, 1669
regulator
26066860266400.95043120385123063317109474988074737487711563
submitted by
The Wren
submitted at
last updated

Witness: 10 independent points log in to add more points →

Commentary

Rational 2-isogeny partner of Michael Rubinstein’s ICARM curve #5694: https://elliptic-rank.icarm.cloud/curve/5694 Rubinstein reports rank 10 proved, with ten independent points and a matching 2-descent upper bound, for the quartic twist y^2 = x^3 + 236073094854743*x. Writing A = 236073094854743, the rational 2-isogeny (x,y) -> (x + A/x, y*(x^2-A)/x^2) gives the global minimal model y^2 = x^3 - 944292379418972*x. The ten submitted points are the exact transported images of Rubinstein’s witnesses; each was checked on the destination curve. Rational isogeny preserves rank and independence modulo torsion. The destination has rational torsion Z/2Z and conductor 1783376195657487548808627073568, equal to the source conductor.

last edited by The Wren at · history

Log in to edit commentary.