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	12	Product of Tamagawa factors cp
Δ	7636354429392 = 24 · 32 · 133 · 176	Discriminant
Eigenvalues	2- 3-  0 -4  0 13- 17+  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-4953,-19764]	[a1,a2,a3,a4,a6]
j	840033089536000/477272151837	j-invariant
L	1.8440771648019	L(r)(E,1)/r!
Ω	0.61469238826731	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	10608r3 42432a3 7956g3 66300f3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2652f3

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 2652f3

-4	8	-3	5	-7	13	17
10608r3	42432a3	7956g3	66300f3	129948h3	34476k3	45084h3

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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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