Cremona's table of elliptic curves

2652 = 2² · 3 · 13 · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 13- 17+	Signs for the Atkin-Lehner involutions
Class	2652f	Isogeny class
Conductor	2652	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	-491735839226112 = -1 · 28 · 34 · 136 · 173	Discriminant
Eigenvalues	2- 3-  0 -4  0 13- 17+  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,19612,-137676]	[a1,a2,a3,a4,a6]
j	3258571509326000/1920843121977	j-invariant
L	1.8440771648019	L(r)(E,1)/r!
Ω	0.30734619413366	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	10608r4 42432a4 7956g4 66300f4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2652f4

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	-4	0	-	+	2	0	6	8	8	0	8	6	-6	-6	-10	2	12	-4	8	18	6	8

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Quadratic twists for elliptic curve 2652f4

-4	8	-3	5	-7	13	17
10608r4	42432a4	7956g4	66300f4	129948h4	34476k4	45084h4

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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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