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	2208h	Isogeny class
Conductor	2208	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	2688	Modular degree for the optimal curve
Δ	-3724440564672 = -1 · 26 · 314 · 233	Discriminant
Eigenvalues	2- 3+  2 -2  2 -2  0 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,2598,76752]	[a1,a2,a3,a4,a6]
Generators	[-22:92:1]	Generators of the group modulo torsion
j	30289632400448/58194383823	j-invariant
L	2.860160215534	L(r)(E,1)/r!
Ω	0.54246550848253	Real period
R	1.7575066499219	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	2208d1 4416m1 6624b1 55200x1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2208h1

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	-2	2	-2	0	-8	-	2	-4	4	2	-4	-8	-2	4	0	-4	-8	6	2	6	-8	-14

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Quadratic twists for elliptic curve 2208h1

-4	8	-3	5	-7	-23
2208d1	4416m1	6624b1	55200x1	108192cf1	50784v1

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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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