Cremona's table of elliptic curves

2233 = 7 · 11 · 29

Field	Data	Notes
Atkin-Lehner	7+ 11+ 29-	Signs for the Atkin-Lehner involutions
Class	2233a	Isogeny class
Conductor	2233	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1344	Modular degree for the optimal curve
Δ	-29354283343 = -1 · 73 · 112 · 294	Discriminant
Eigenvalues	-1  0 -2 7+ 11+  6 -2 -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,584,6050]	[a1,a2,a3,a4,a6]
j	22062729659823/29354283343	j-invariant
L	0.39694962836734	L(r)(E,1)/r!
Ω	0.79389925673468	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	35728y1 20097h1 55825l1 15631c1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2233a1

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
-1	0	-2	+	+	6	-2	-8	0	-	-4	-2	-2	-4	-4	-10	12	2	12	8	-10	0	12	6	-2

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Quadratic twists for elliptic curve 2233a1

-4	-3	5	-7	-11	29
35728y1	20097h1	55825l1	15631c1	24563g1	64757e1

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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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