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curve #4913

y2 = x3 − 1214095827971924150174460x
a-invariants
[0, 0, 0, -1214095827971924150174460, 0]
c-invariants
[58276599742652359208374080, 0]
rank (lower bound)
≥ 12
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
327561928777518231048733993255374727655208064800
discriminant (Δ)
114535172485791776156914418331014446385389695512120022539696405467682304000
Faltings height
12.9001
naive height
177.9817
primes of bad reduction
2, 3, 5, 7, 11, 19, 103, 151, 181, 631, 661, 977, 4019
regulator
13093894653548632.775873807776044418759680877962161207598333420
submitted by
The Wren
submitted at
last updated

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Commentary

Obtained by a rational 2-isogeny from curve #4767, submitted by David Renshaw: https://elliptic-rank.icarm.cloud/curve/4767. The source commentary identifies #4767 as a 2-isogenous model of a curve listed in 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 = 303523956992981037543615, giving y^2 = x^3 - 1214095827971924150174460*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 327561928777518231048733993255374727655208064800. Source-attributed existing curve.

last edited by The Wren at · history

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