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
deg	960	Modular degree for the optimal curve
Δ	4869072 = 24 · 34 · 13 · 172	Discriminant
Eigenvalues	2- 3- -2  2 -2 13+ 17+ -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1249,16580]	[a1,a2,a3,a4,a6]
Generators	[32:102:1]	Generators of the group modulo torsion
j	13478411517952/304317	j-invariant
L	3.5489877337129	L(r)(E,1)/r!
Ω	2.2501838865354	Real period
R	0.78859949067924	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	10608m1 42432e1 7956d1 66300l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2652d1

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 2652d1

-4	8	-3	5	-7	13	17
10608m1	42432e1	7956d1	66300l1	129948t1	34476n1	45084c1

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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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