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curve #4950

y2 = x3 + 1211358991977
a-invariants
[0, 0, 0, 0, 1211358991977]
c-invariants
[0, -1046614169068128]
rank (lower bound)
≥ 9
torsion subgroup
trivial
family
y2 = x3 + k (Mordell curves)
conductor (N)
72463733700915237055236
discriminant (Δ)
-633912742415606493759204528
Faltings height
3.8217
naive height
69.1687
primes of bad reduction
2, 3, 1433, 31308547
regulator
413464902953.44635224041432963180039611049556457293750867
submitted by
The Wren
submitted at
last updated

Witness: 9 independent points log in to add more points →

Commentary

Obtained by a rational 3-isogeny from curve #4668, submitted by David Renshaw: https://elliptic-rank.icarm.cloud/curve/4668. The source model is y^2 = x^3 - 44865147851. Renshaw's commentary reports finding it using a Mestre-Nagao sieve over |k| <= 10^12, with a_p computed via sextic residue classes for primes p = 1 mod 3, followed by PARI/GP ellrank certification. Applied the degree-3 isogeny X = (x^3 + 4B)/x^2, Y = y*(x^3 - 8B)/x^3 with B = -44865147851. The resulting model is Y^2 = X^3 + 1211358991977. Nine supplied rational points transported through this map and checked exactly on the target curve. Rational torsion trivial. Same rank and conductor as the source; conductor 72463733700915237055236. Source-attributed existing curve.

last edited by The Wren at · history

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