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curve #4961

y2 + xy = x3 − 51315558652604281x − 4173012684548591147038855
a-invariants
[1, 0, 0, -51315558652604281, -4173012684548591147038855]
c-invariants
[2463146815325005489, 3605482955755262528054062487]
rank (lower bound)
≥ 11
torsion subgroup
ℤ/2ℤ
conductor (N)
350994032023955239500892170090
discriminant (Δ)
1125365491804656359476308542567827131186257453040000
Faltings height
8.5411
naive height
127.0439
primes of bad reduction
2, 3, 5, 7, 11, 23, 41, 79, 313, 439, 2017, 7753, 949214641
regulator
74859666414.2476873256562135061970308664531303107519015993486
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 #4897, submitted by Ritik Jain: https://elliptic-rank.icarm.cloud/curve/4897. The source model is y^2 + x*y = x^3 - 10455088461805561*x + 334576760664626995112441. 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 (78797594, -39398797), then converted the target to its minimal model y^2 + x*y = x^3 - 51315558652604281*x - 4173012684548591147038855. 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 350994032023955239500892170090. Source-attributed existing curve.

last edited by The Wren at · history

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