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curve #4912

y2 = x3 − 715970874943386994467852x
a-invariants
[0, 0, 0, -715970874943386994467852, 0]
c-invariants
[34366601997282575734456896, 0]
rank (lower bound)
≥ 12
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
113914287503822021953053632003640671122813665312
discriminant (Δ)
23489081882687228749445503846959090657760592328797915470548586868606349312
Faltings height
12.7680
naive height
176.3974
primes of bad reduction
2, 3, 19, 43, 47, 67, 109, 127, 137, 233, 593, 29501
regulator
6336990891876100.5699352939549948851811083155583091164254186468
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 #4766, submitted by David Renshaw: https://elliptic-rank.icarm.cloud/curve/4766. The source commentary identifies #4766 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 = 178992718735846748616963, giving y^2 = x^3 - 715970874943386994467852*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 113914287503822021953053632003640671122813665312. Source-attributed existing curve.

last edited by The Wren at · history

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