Cremona's table of elliptic curves

Curve 21648bd1

21648 = 24 · 3 · 11 · 41



Data for elliptic curve 21648bd1

Field Data Notes
Atkin-Lehner 2- 3- 11+ 41+ Signs for the Atkin-Lehner involutions
Class 21648bd Isogeny class
Conductor 21648 Conductor
∏ cp 8 Product of Tamagawa factors cp
deg 322560 Modular degree for the optimal curve
Δ 54504490115530752 = 226 · 3 · 115 · 412 Discriminant
Eigenvalues 2- 3- -4 -2 11+ -2  2  8 Hecke eigenvalues for primes up to 20
Equation [0,1,0,-189040,-29637676] [a1,a2,a3,a4,a6]
Generators [400500:4163878:729] Generators of the group modulo torsion
j 182400988413112561/13306760282112 j-invariant
L 3.9219979126712 L(r)(E,1)/r!
Ω 0.2300151081287 Real period
R 8.5255223984608 Regulator
r 1 Rank of the group of rational points
S 1 (Analytic) order of Ш
t 2 Number of elements in the torsion subgroup
Twists 2706n1 86592cl1 64944by1 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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