Cremona's table of elliptic curves

8652 = 2² · 3 · 7 · 103

Field	Data	Notes
Atkin-Lehner	2- 3+ 7+ 103-	Signs for the Atkin-Lehner involutions
Class	8652b	Isogeny class
Conductor	8652	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	13859258112 = 28 · 36 · 7 · 1032	Discriminant
Eigenvalues	2- 3+ -4 7+ -2  2  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-396060,-95805864]	[a1,a2,a3,a4,a6]
Generators	[1006:22866:1]	Generators of the group modulo torsion
j	26839090376930139856/54137727	j-invariant
L	2.2724511078302	L(r)(E,1)/r!
Ω	0.19030895195298	Real period
R	3.9802841371184	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	34608bd2 25956i2 60564j2	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 8652b2

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
-	+	-4	+	-2	2	0	-4	2	-2	-8	10	-12	12	-4	6	-4	14	-16	-6	14	12	16	16	-10

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Quadratic twists for elliptic curve 8652b2

-4	-3	-7
34608bd2	25956i2	60564j2

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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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