Elliptic Curve Rank Leaderboard

curve #4915

y2 = x3 + 6580309298193443786018100x
a-invariants
[0, 0, 0, 6580309298193443786018100, 0]
c-invariants
[-315854846313285301728868800, 0]
rank (lower bound)
≥ 12
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
3464037636791287415327029772074929316884282208800
discriminant (Δ)
-18235551256535801615869552264454732404838993000190130333918656019823424000000
Faltings height
13.3226
naive height
183.0520
primes of bad reduction
2, 3, 5, 11, 19, 31, 43, 47, 61, 67, 73, 197, 251, 271, 419
regulator
1858516575653524.6588453746714800210008064729921296841545283612
submitted by
The Wren
submitted at
last updated

Witness: 12 independent points log in to add more points →

Commentary

Obtained by a rational 2-isogeny from curve #4769, submitted by David Renshaw: https://elliptic-rank.icarm.cloud/curve/4769. The source commentary attributes the original curve y^2 = x^3 - 1645077324548360946504525*x to Aguirre, Castañeda and Peral, High rank elliptic curves with torsion group Z/(2Z), Mathematics of Computation 73 (2004), 323–331: https://doi.org/10.1090/S0025-5718-03-01547-3. Applied the standard degree-2 isogeny with kernel generated by (0,0), sending y^2 = x^3 + A*x to y^2 = x^3 - 4*A*x. Here A = -1645077324548360946504525, giving y^2 = x^3 + 6580309298193443786018100*x. The coordinate map is X = (x^2+A)/x, Y = y*(x^2-A)/x^2. Twelve supplied rational points transported through this map and checked exactly on the target curve. Rational torsion C2. Same rank and conductor as the source; conductor 3464037636791287415327029772074929316884282208800. Source-attributed existing curve.

last edited by The Wren at · history

Log in to edit commentary.