Cremona's table of elliptic curves

2829 = 3 · 23 · 41

Field	Data	Notes
Atkin-Lehner	3- 23+ 41-	Signs for the Atkin-Lehner involutions
Class	2829g	Isogeny class
Conductor	2829	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1728	Modular degree for the optimal curve
Δ	-1656670887 = -1 · 34 · 233 · 412	Discriminant
Eigenvalues	1 3-  2 -2 -6  6  0 -6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,130,1883]	[a1,a2,a3,a4,a6]
Generators	[3:46:1]	Generators of the group modulo torsion
j	245667233447/1656670887	j-invariant
L	4.7810614680002	L(r)(E,1)/r!
Ω	1.0875660063402	Real period
R	2.1980557686283	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	45264k1 8487l1 70725g1 65067t1	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 2829g1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
1	-	2	-2	-6	6	0	-6	+	2	-8	2	-	-4	0	-12	-12	-6	-2	12	10	-2	-16	8	-12

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Quadratic twists for elliptic curve 2829g1

-4	-3	5	-23	41
45264k1	8487l1	70725g1	65067t1	115989c1

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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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