Cremona's table of elliptic curves

2173 = 41 · 53

Field	Data	Notes
Atkin-Lehner	41- 53+	Signs for the Atkin-Lehner involutions
Class	2173b	Isogeny class
Conductor	2173	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	756	Modular degree for the optimal curve
Δ	3652813 = 413 · 53	Discriminant
Eigenvalues	2  3  0  2  0  0 -6  7	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-55,127]	[a1,a2,a3,a4,a6]
j	18399744000/3652813	j-invariant
L	7.0893800928548	L(r)(E,1)/r!
Ω	2.3631266976183	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	34768f1 19557e1 54325f1 106477b1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2173b1

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	3	0	2	0	0	-6	7	4	2	-2	-7	-	4	4	+	-5	10	-9	-8	2	-1	-10	10	-8

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Quadratic twists for elliptic curve 2173b1

-4	-3	5	-7	41	53
34768f1	19557e1	54325f1	106477b1	89093f1	115169c1

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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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