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curve #4941

y2 = x3 + 214241769x
a-invariants
[0, 0, 0, 214241769, 0]
c-invariants
[-10283604912, 0]
rank (lower bound)
≥ 4
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
13711473216
discriminant (Δ)
-629350252790274024816614976
Faltings height
3.8317
naive height
69.1615
primes of bad reduction
2, 3, 7, 17, 41
regulator
2764.672501466871728932331803378789625846240685
submitted by
The Wren
submitted at
last updated

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Commentary

Obtained by a rational 2-isogeny from curve #15, submitted by David Renshaw: https://elliptic-rank.icarm.cloud/curve/15. The source commentary attributes the original curve y^2 = x^3 - 856967076*x to Wiman (1945), via Dujella's elliptic-curve rank-record tables. Applied the standard degree-2 isogeny with kernel generated by (0,0), followed by the rational change of coordinates dividing x by 4 and y by 8. With A = -856967076, the combined map is X = (x^2+A)/(4*x), Y = y*(x^2-A)/(8*x^2), giving y^2 = x^3 + 214241769*x. Four 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 13711473216. Source-attributed existing curve.

last edited by The Wren at · history

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