Cremona's table of elliptic curves

5208 = 2³ · 3 · 7 · 31

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 31+	Signs for the Atkin-Lehner involutions
Class	5208l	Isogeny class
Conductor	5208	Conductor
∏ cp	3	Product of Tamagawa factors cp
Δ	11999232 = 211 · 33 · 7 · 31	Discriminant
Eigenvalues	2- 3- -2 7+  4 -2  2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-249984,-48191328]	[a1,a2,a3,a4,a6]
Generators	[867:19686:1]	Generators of the group modulo torsion
j	843591384940292354/5859	j-invariant
L	4.0483789082588	L(r)(E,1)/r!
Ω	0.21351154180228	Real period
R	6.3203123573334	Regulator
r	1	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	10416f3 41664e4 15624g3 36456t4	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 5208l3

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

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Quadratic twists for elliptic curve 5208l3

-4	8	-3	-7
10416f3	41664e4	15624g3	36456t4

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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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