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curve #4907

y2 = x3 + 3688123365423x
a-invariants
[0, 0, 0, 3688123365423, 0]
c-invariants
[-177029921540304, 0]
rank (lower bound)
≥ 8
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
48363569630503379882556192
discriminant (Δ)
-3210674601411390996180528791957052285888
Faltings height
6.2701
naive height
98.4220
primes of bad reduction
2, 3, 7, 23, 71, 113, 281, 1129
regulator
78649085311.3971645931432292787981615694350125091197828
submitted by
The Wren
submitted at
last updated

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Commentary

Obtained by a rational 2-isogeny from curve #4762, submitted by David Renshaw: https://elliptic-rank.icarm.cloud/curve/4762. The source commentary attributes the original curve y^2 = x^3 - 14752493461692*x to Aguirre, Castañeda and Peral, High rank elliptic curves of the form y^2=x^3+Bx, Revista Matemática Complutense 13 (2000), 17–31: https://revistas.ucm.es/index.php/REMA/article/view/REMA0000120017A. 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 = -14752493461692, the combined map is X = (x^2+A)/(4*x), Y = y*(x^2-A)/(8*x^2), giving y^2 = x^3 + 3688123365423*x. Eight 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 48363569630503379882556192. Source-attributed existing curve.

last edited by The Wren at · history

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