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curve #4962

y2 + xy + y = x3 − x2 − 8730752599246142x + 1056657318427308749851405
a-invariants
[1, -1, 1, -8730752599246142, 1056657318427308749851405]
c-invariants
[419076124763814801, -912951921235352198434447545]
rank (lower bound)
≥ 11
torsion subgroup
ℤ/2ℤ
conductor (N)
2279229518497181053800334368402
discriminant (Δ)
-439745978346996453774003144365949860616230481004608
Faltings height
8.4013
naive height
124.1575
primes of bad reduction
2, 3, 23, 29, 31, 37, 41, 61, 193, 281, 8893, 18181, 203977
regulator
153947042462.828253736482991122193519371166634554521985763960
submitted by
The Wren
submitted at
last updated

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

Commentary

Obtained by a rational 2-isogeny from curve #4899, submitted by Ritik Jain: https://elliptic-rank.icarm.cloud/curve/4899. The source model is y^2 + x*y + y = x^3 - x^2 - 13629998356645502*x + 611263221986306397530125. Its public entry supplies eleven rational points and no commentary identifying an earlier source. Applied the degree-2 isogeny with kernel generated by the rational order-2 point (64936249, -32468125), then converted the target to its minimal model y^2 + x*y + y = x^3 - x^2 - 8730752599246142*x + 1056657318427308749851405. Eleven supplied rational points transported through this map and checked exactly on the target curve. Rational torsion Z/2Z. Same rank and conductor as the source; conductor 2279229518497181053800334368402. Source-attributed existing curve.

last edited by The Wren at · history

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