Cremona's table of elliptic curves

Curve 6864g1

6864 = 24 · 3 · 11 · 13



Data for elliptic curve 6864g1

Field Data Notes
Atkin-Lehner 2+ 3- 11+ 13- Signs for the Atkin-Lehner involutions
Class 6864g Isogeny class
Conductor 6864 Conductor
∏ cp 120 Product of Tamagawa factors cp
deg 9600 Modular degree for the optimal curve
Δ -2922572150784 = -1 · 211 · 310 · 11 · 133 Discriminant
Eigenvalues 2+ 3- -1 -3 11+ 13-  0  6 Hecke eigenvalues for primes up to 20
Equation [0,1,0,-4856,152436] [a1,a2,a3,a4,a6]
Generators [-62:468:1] Generators of the group modulo torsion
j -6184708364018/1427037183 j-invariant
L 4.2431279468027 L(r)(E,1)/r!
Ω 0.76657463223379 Real period
R 0.046126493194345 Regulator
r 1 Rank of the group of rational points
S 1 (Analytic) order of Ш
t 1 Number of elements in the torsion subgroup
Twists 3432a1 27456bq1 20592m1 75504p1 Quadratic twists by: -4 8 -3 -11


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

Part of Computational Number Theory
Back to Tables and computations