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curve #4903

y2 = x3 + 6308188168x
a-invariants
[0, 0, 0, 6308188168, 0]
c-invariants
[-302793032064, 0]
rank (lower bound)
≥ 7
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
159172951851580784896
discriminant (Δ)
-16065486904572409590033604968448
Faltings height
4.6773
naive height
79.3089
primes of bad reduction
2, 41, 2593, 7417
regulator
128134344.2467897666674060752330878106797078614871174
submitted by
The Wren
submitted at
last updated

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Commentary

Obtained by a rational 2-isogeny from curve #4758, submitted by David Renshaw: https://elliptic-rank.icarm.cloud/curve/4758. The original curve y^2 = x^3 - 1577047042*x appears as the rank-7 example in Table 2, Section 6.1, of Julián Aguirre, Álvaro Lozano-Robledo and Juan Carlos Peral, Elliptic curves of maximal rank: https://alozano.clas.uconn.edu/wp-content/uploads/sites/490/2014/01/ALP-2-23-07.pdf. 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 = -1577047042, giving y^2 = x^3 + 6308188168*x. The coordinate map is X = (x^2+A)/x, Y = y*(x^2-A)/x^2. Seven 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 159172951851580784896. Source-attributed existing curve.

last edited by The Wren at · history

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