Cremona's table of elliptic curves

2173 = 41 · 53

Field	Data	Notes
Atkin-Lehner	41- 53-	Signs for the Atkin-Lehner involutions
Class	2173c	Isogeny class
Conductor	2173	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	84	Modular degree for the optimal curve
Δ	2173 = 41 · 53	Discriminant
Eigenvalues	0  1  0  4 -6  2  2 -3	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-3,-2]	[a1,a2,a3,a4,a6]
Generators	[-2:0:1]	Generators of the group modulo torsion
j	4096000/2173	j-invariant
L	3.1663455508879	L(r)(E,1)/r!
Ω	3.7521862641651	Real period
R	0.84386683601712	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	34768g1 19557a1 54325b1 106477c1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2173c1

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	4	-6	2	2	-3	-4	8	-4	-3	-	-4	-4	-	-13	0	-11	-12	16	5	-2	6	4

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Quadratic twists for elliptic curve 2173c1

-4	-3	5	-7	41	53
34768g1	19557a1	54325b1	106477c1	89093a1	115169a1

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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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