Cremona's table of elliptic curves

45504 = 2⁶ · 3² · 79

Field	Data	Notes
Atkin-Lehner	2- 3- 79+	Signs for the Atkin-Lehner involutions
Class	45504bi	Isogeny class
Conductor	45504	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-17666478784512 = -1 · 214 · 37 · 793	Discriminant
Eigenvalues	2- 3-  0  1 -3 -5  3  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-3900,-222896]	[a1,a2,a3,a4,a6]
Generators	[716:19080:1]	Generators of the group modulo torsion
j	-549250000/1479117	j-invariant
L	5.4311370368277	L(r)(E,1)/r!
Ω	0.28050092454809	Real period
R	4.8405696394548	Regulator
r	1	Rank of the group of rational points
S	1.0000000000003	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	45504v2 11376j2 15168o2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 45504bi2

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	-3	-5	3	2	-3	9	-2	-8	-6	11	-6	6	6	10	8	-12	11	+	3	12	-1

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Quadratic twists for elliptic curve 45504bi2

-4	8	-3
45504v2	11376j2	15168o2

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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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