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	2208g	Isogeny class
Conductor	2208	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	2437632 = 29 · 32 · 232	Discriminant
Eigenvalues	2+ 3-  0  0 -2 -2 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-88,-340]	[a1,a2,a3,a4,a6]
Generators	[11:12:1]	Generators of the group modulo torsion
j	148877000/4761	j-invariant
L	3.5383075270037	L(r)(E,1)/r!
Ω	1.5603395267541	Real period
R	2.2676523066517	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	2208a2 4416t2 6624d2 55200bm2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2208g2

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

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Quadratic twists for elliptic curve 2208g2

-4	8	-3	5	-7	-23
2208a2	4416t2	6624d2	55200bm2	108192i2	50784h2

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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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