Cremona's table of elliptic curves

Curve 128271q1

128271 = 3 · 11 · 132 · 23



Data for elliptic curve 128271q1

Field Data Notes
Atkin-Lehner 3- 11- 13+ 23+ Signs for the Atkin-Lehner involutions
Class 128271q Isogeny class
Conductor 128271 Conductor
∏ cp 72 Product of Tamagawa factors cp
deg 2515968 Modular degree for the optimal curve
Δ -1.7038069836139E+19 Discriminant
Eigenvalues -1 3-  0 -4 11- 13+  0  4 Hecke eigenvalues for primes up to 20
Equation [1,0,0,-743688,316758519] [a1,a2,a3,a4,a6]
Generators [495:-8613:1] Generators of the group modulo torsion
j -9424014732015625/3529882751967 j-invariant
L 3.9654953095254 L(r)(E,1)/r!
Ω 0.20622108442358 Real period
R 1.0682966599527 Regulator
r 1 Rank of the group of rational points
S 0.99999999669599 (Analytic) order of Ш
t 2 Number of elements in the torsion subgroup
Twists 9867i1 Quadratic twists by: 13


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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