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	2652d	Isogeny class
Conductor	2652	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-32521072896 = -1 · 28 · 32 · 132 · 174	Discriminant
Eigenvalues	2- 3- -2  2 -2 13+ 17+ -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1204,17876]	[a1,a2,a3,a4,a6]
Generators	[11:78:1]	Generators of the group modulo torsion
j	-754612278352/127035441	j-invariant
L	3.5489877337129	L(r)(E,1)/r!
Ω	1.1250919432677	Real period
R	1.5771989813585	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	10608m2 42432e2 7956d2 66300l2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2652d2

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
-	-	-2	2	-2	+	+	-6	4	-6	-2	10	-2	-4	-6	-10	2	-10	10	-6	10	0	-2	-10	10

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Quadratic twists for elliptic curve 2652d2

-4	8	-3	5	-7	13	17
10608m2	42432e2	7956d2	66300l2	129948t2	34476n2	45084c2

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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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