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curve #1375

y2 = x3 + x2 − 7739356160225544477844001x + 8287153029037256910365409890880643455
a-invariants
[0, 1, 0, -7739356160225544477844001, 8287153029037256910365409890880643455]
rank (lower bound)
≥ 11
torsion subgroup
ℤ/2ℤ
conductor (N)
23354778245864734004307533064634560
discriminant (Δ)
638893263333002723265169980004644396987249666267748099994354531205120
Faltings height
12.7644
naive height
183.5387
primes of bad reduction
2, 3, 5, 11, 13, 19, 23, 29, 31, 41, 43, 53, 61, 71, 97, 101, 103, 113, 139, 181, 373
regulator
134626083002.675186460383627562439976572126426296192064131948
submitted by
jesper-petersen
submitted at
last updated

Witness: 11 independent points log in to add more points →

Commentary

Obtained from curve #1202, submitted by Noam Elkies, which has rank at least 11 and torsion \(\mathbf Z/2\mathbf Z\times\mathbf Z/2\mathbf Z\). Quotienting by the rational 2-torsion point \((-803153556053,0)\) gives the 2-isogenous curve \(y^2=x^3+4818921336316x^2+1311454974983248973284x\). Its global minimal model has ainvs \([0,1,0,-7739356160225544477844001,8287153029037256910365409890880643455]\), torsion \(\mathbf Z/2\mathbf Z\), and conductor \(23354778245864734004307533064634560\). The eleven independent points on #1202 were mapped through the 2-isogeny, giving eleven independent points on the quotient. The isogeny, minimal model, conductor, torsion and image points were verified in Magma.

last edited by jesper-petersen at · history

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