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	5208j	Isogeny class
Conductor	5208	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	457304064 = 211 · 3 · 74 · 31	Discriminant
Eigenvalues	2- 3+ -2 7+  0  2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3984,98124]	[a1,a2,a3,a4,a6]
Generators	[233:3430:1]	Generators of the group modulo torsion
j	3415550840354/223293	j-invariant
L	2.7280759620316	L(r)(E,1)/r!
Ω	1.5821534833343	Real period
R	3.4485604472233	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	10416k3 41664br4 15624j3 36456z4	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 5208j3

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

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Quadratic twists for elliptic curve 5208j3

-4	8	-3	-7
10416k3	41664br4	15624j3	36456z4

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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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