Cremona's table of elliptic curves

2208 = 2⁵ · 3 · 23

Field	Data	Notes
Atkin-Lehner	2+ 3- 23+	Signs for the Atkin-Lehner involutions
Class	2208f	Isogeny class
Conductor	2208	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	21938688 = 29 · 34 · 232	Discriminant
Eigenvalues	2+ 3-  4  4 -6  6 -2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-856,-9928]	[a1,a2,a3,a4,a6]
j	135638288072/42849	j-invariant
L	3.5302630494468	L(r)(E,1)/r!
Ω	0.88256576236169	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2208c2 4416s2 6624j2 55200bu2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2208f2

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

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Quadratic twists for elliptic curve 2208f2

-4	8	-3	5	-7	-23
2208c2	4416s2	6624j2	55200bu2	108192g2	50784r2

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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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