Cremona's table of elliptic curves

Curve 129344z1

129344 = 26 · 43 · 47



Data for elliptic curve 129344z1

Field Data Notes
Atkin-Lehner 2- 43- 47+ Signs for the Atkin-Lehner involutions
Class 129344z Isogeny class
Conductor 129344 Conductor
∏ cp 2 Product of Tamagawa factors cp
deg 22272 Modular degree for the optimal curve
Δ 2069504 = 210 · 43 · 47 Discriminant
Eigenvalues 2-  0  1  4 -6 -6 -3 -1 Hecke eigenvalues for primes up to 20
Equation [0,0,0,-32,-8] [a1,a2,a3,a4,a6]
Generators [6:4:1] Generators of the group modulo torsion
j 3538944/2021 j-invariant
L 6.2806223532186 L(r)(E,1)/r!
Ω 2.173358333524 Real period
R 1.4449118306038 Regulator
r 1 Rank of the group of rational points
S 1.0000000026619 (Analytic) order of Ш
t 1 Number of elements in the torsion subgroup
Twists 129344i1 32336f1 Quadratic twists by: -4 8


Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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