Cremona's table of elliptic curves

4292 = 2² · 29 · 37

Field	Data	Notes
Atkin-Lehner	2- 29- 37+	Signs for the Atkin-Lehner involutions
Class	4292b	Isogeny class
Conductor	4292	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	1920	Modular degree for the optimal curve
Δ	6699365632 = 28 · 294 · 37	Discriminant
Eigenvalues	2- -1 -2 -3  1  2  4  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-509,-1847]	[a1,a2,a3,a4,a6]
Generators	[27:58:1]	Generators of the group modulo torsion
j	57080799232/26169397	j-invariant
L	2.3533140171169	L(r)(E,1)/r!
Ω	1.0497606457549	Real period
R	0.18681353908575	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	17168k1 68672f1 38628c1 107300l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4292b1

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	-3	1	2	4	4	-6	-	8	+	3	-10	9	-3	4	8	8	3	-5	-8	7	-12	-4

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Quadratic twists for elliptic curve 4292b1

-4	8	-3	5	29
17168k1	68672f1	38628c1	107300l1	124468d1

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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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