Cremona's table of elliptic curves

2173 = 41 · 53

Field	Data	Notes
Atkin-Lehner	41- 53+	Signs for the Atkin-Lehner involutions
Class	2173a	Isogeny class
Conductor	2173	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	304	Modular degree for the optimal curve
Δ	-89093 = -1 · 412 · 53	Discriminant
Eigenvalues	1 -1 -2 -4 -6 -1 -1  1	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-131,526]	[a1,a2,a3,a4,a6]
Generators	[6:-2:1] [14:34:1]	Generators of the group modulo torsion
j	-251598106297/89093	j-invariant
L	3.2548189950596	L(r)(E,1)/r!
Ω	3.3327526665603	Real period
R	0.48830791251281	Regulator
r	2	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	34768e1 19557c1 54325e1 106477a1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2173a1

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	-1	-2	-4	-6	-1	-1	1	3	-9	0	1	-	-8	-2	+	0	-6	-4	-5	-4	-11	3	6	-17

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Quadratic twists for elliptic curve 2173a1

-4	-3	5	-7	41	53
34768e1	19557c1	54325e1	106477a1	89093c1	115169b1

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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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