Cremona's table of elliptic curves

1173 = 3 · 17 · 23

Field	Data	Notes
Atkin-Lehner	3+ 17- 23+	Signs for the Atkin-Lehner involutions
Class	1173b	Isogeny class
Conductor	1173	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	520	Modular degree for the optimal curve
Δ	623380293 = 313 · 17 · 23	Discriminant
Eigenvalues	0 3+  2  5  2 -1 17- -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-527,4679]	[a1,a2,a3,a4,a6]
j	16217331171328/623380293	j-invariant
L	1.611162816281	L(r)(E,1)/r!
Ω	1.611162816281	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	18768bb1 75072br1 3519c1 29325p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1173b1

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	+	2	5	2	-1	-	-2	+	1	-2	3	6	2	4	-3	-8	5	16	3	-4	-9	7	7	-13

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Quadratic twists for elliptic curve 1173b1

-4	8	-3	5	-7	17	-23
18768bb1	75072br1	3519c1	29325p1	57477k1	19941j1	26979b1

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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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