Cremona's table of elliptic curves

Curve 51984v4

51984 = 24 · 32 · 192



Data for elliptic curve 51984v4

Field Data Notes
Atkin-Lehner 2+ 3- 19- Signs for the Atkin-Lehner involutions
Class 51984v Isogeny class
Conductor 51984 Conductor
∏ cp 8 Product of Tamagawa factors cp
Δ 105358685948928 = 210 · 37 · 196 Discriminant
Eigenvalues 2+ 3-  2  0  4  2 -2 19- Hecke eigenvalues for primes up to 20
Equation [0,0,0,-209019,-36777958] [a1,a2,a3,a4,a6]
Generators [-842195366194:99089194680:3170044709] Generators of the group modulo torsion
j 28756228/3 j-invariant
L 7.8278171132995 L(r)(E,1)/r!
Ω 0.22328308908832 Real period
R 17.528907238817 Regulator
r 1 Rank of the group of rational points
S 1.0000000000062 (Analytic) order of Ш
t 2 Number of elements in the torsion subgroup
Twists 25992bc4 17328f4 144b4 Quadratic twists by: -4 -3 -19


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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