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	2829b	Isogeny class
Conductor	2829	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	5280	Modular degree for the optimal curve
Δ	71946700821 = 33 · 23 · 415	Discriminant
Eigenvalues	0 3+ -1  1  4  0  0 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-52371,4630493]	[a1,a2,a3,a4,a6]
j	15885635914127540224/71946700821	j-invariant
L	0.96501925246786	L(r)(E,1)/r!
Ω	0.96501925246786	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	45264o1 8487g1 70725k1 65067c1	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 2829b1

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
0	+	-1	1	4	0	0	-5	-	-10	8	10	+	-4	1	12	-6	0	-7	-13	3	8	4	6	14

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Quadratic twists for elliptic curve 2829b1

-4	-3	5	-23	41
45264o1	8487g1	70725k1	65067c1	115989i1

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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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