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	2208c	Isogeny class
Conductor	2208	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1024	Modular degree for the optimal curve
Δ	-9657792 = -1 · 26 · 38 · 23	Discriminant
Eigenvalues	2+ 3+  4 -4  6  6 -2  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-46,208]	[a1,a2,a3,a4,a6]
j	-171879616/150903	j-invariant
L	2.1024173728995	L(r)(E,1)/r!
Ω	2.1024173728995	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	2208f1 4416bb1 6624f1 55200ch1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2208c1

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 2208c1

-4	8	-3	5	-7	-23
2208f1	4416bb1	6624f1	55200ch1	108192x1	50784g1

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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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