Cremona's table of elliptic curves

Curve 127296cb1

127296 = 26 · 32 · 13 · 17



Data for elliptic curve 127296cb1

Field Data Notes
Atkin-Lehner 2- 3- 13+ 17+ Signs for the Atkin-Lehner involutions
Class 127296cb Isogeny class
Conductor 127296 Conductor
∏ cp 8 Product of Tamagawa factors cp
deg 65536 Modular degree for the optimal curve
Δ -6434049024 = -1 · 210 · 37 · 132 · 17 Discriminant
Eigenvalues 2- 3-  2  2 -4 13+ 17+ -8 Hecke eigenvalues for primes up to 20
Equation [0,0,0,456,920] [a1,a2,a3,a4,a6]
Generators [830:23920:1] Generators of the group modulo torsion
j 14047232/8619 j-invariant
L 7.8471989982606 L(r)(E,1)/r!
Ω 0.82463228740127 Real period
R 4.757998857265 Regulator
r 1 Rank of the group of rational points
S 1.0000000045905 (Analytic) order of Ш
t 2 Number of elements in the torsion subgroup
Twists 127296e1 31824p1 42432bo1 Quadratic twists by: -4 8 -3


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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