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	2233b	Isogeny class
Conductor	2233	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	336	Modular degree for the optimal curve
Δ	-20657483 = -1 · 7 · 112 · 293	Discriminant
Eigenvalues	0  1  0 7- 11+  2  6 -7	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-63,271]	[a1,a2,a3,a4,a6]
Generators	[31:170:1]	Generators of the group modulo torsion
j	-28094464000/20657483	j-invariant
L	3.0774335441639	L(r)(E,1)/r!
Ω	1.9850402489624	Real period
R	2.3254693796051	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	35728v1 20097k1 55825d1 15631b1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2233b1

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	1	0	-	+	2	6	-7	-3	-	-4	2	9	-4	-9	9	-6	2	-13	-9	-1	-10	-6	-15	-7

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Quadratic twists for elliptic curve 2233b1

-4	-3	5	-7	-11	29
35728v1	20097k1	55825d1	15631b1	24563a1	64757h1

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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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