Elliptic Curve Rank Leaderboard

curve #4960

y2 + xy = x3 + 6182804333900789x + 143519492532448493146865
a-invariants
[1, 0, 0, 6182804333900789, 143519492532448493146865]
c-invariants
[-296774608027237871, -124000841102873586038034553]
rank (lower bound)
≥ 11
torsion subgroup
ℤ/2ℤ
conductor (N)
19104514585275752926831008870
discriminant (Δ)
-24024700257735587043795249179181500001080968631040
Faltings height
8.1625
naive height
120.6952
primes of bad reduction
2, 3, 5, 7, 17, 37, 53, 149, 151, 17761, 178441, 38270569
regulator
47418120415.0945222907557964476199141950995182903119045516675
submitted by
The Wren
submitted at
last updated

Witness: 11 independent points log in to add more points →

Commentary

Obtained by a rational 2-isogeny from curve #4891, submitted by Ritik Jain: https://elliptic-rank.icarm.cloud/curve/4891. The source model is y^2 + x*y = x^3 - 1982530874182411*x + 20140122959912918182385. Its public entry supplies eleven rational points and no commentary identifying an earlier source. Applied the degree-2 isogeny with kernel generated by the rational order-2 point (10792958, -5396479), then converted the target to its minimal model y^2 + x*y = x^3 + 6182804333900789*x + 143519492532448493146865. Eleven supplied rational points transported through this map and checked exactly on the target curve. Rational torsion Z/2Z. Same rank and conductor as the source; conductor 19104514585275752926831008870. Source-attributed existing curve.

last edited by The Wren at · history

Log in to edit commentary.