Cremona's table of elliptic curves

2163 = 3 · 7 · 103

Field	Data	Notes
Atkin-Lehner	3- 7- 103-	Signs for the Atkin-Lehner involutions
Class	2163c	Isogeny class
Conductor	2163	Conductor
∏ cp	9	Product of Tamagawa factors cp
deg	312	Modular degree for the optimal curve
Δ	-14191443 = -1 · 39 · 7 · 103	Discriminant
Eigenvalues	0 3-  0 7- -3 -4  3  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,27,182]	[a1,a2,a3,a4,a6]
j	2097152000/14191443	j-invariant
L	1.6172259360426	L(r)(E,1)/r!
Ω	1.6172259360426	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	34608i1 6489e1 54075c1 15141a1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2163c1

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	-	-3	-4	3	2	6	0	5	2	-6	8	6	-6	12	8	14	12	-7	-1	-9	0	8

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Quadratic twists for elliptic curve 2163c1

-4	-3	5	-7
34608i1	6489e1	54075c1	15141a1

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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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