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	1173f	Isogeny class
Conductor	1173	Conductor
∏ cp	5	Product of Tamagawa factors cp
deg	120	Modular degree for the optimal curve
Δ	95013 = 35 · 17 · 23	Discriminant
Eigenvalues	-2 3-  0  1  0 -5 17- -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-18,20]	[a1,a2,a3,a4,a6]
Generators	[0:4:1]	Generators of the group modulo torsion
j	681472000/95013	j-invariant
L	1.6560105087818	L(r)(E,1)/r!
Ω	3.2478519551486	Real period
R	0.10197573852814	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	18768p1 75072p1 3519f1 29325f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1173f1

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	-	0	1	0	-5	-	-8	+	1	0	-1	-2	2	-4	-3	4	1	-4	3	8	-1	-9	-1	3

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Quadratic twists for elliptic curve 1173f1

-4	8	-3	5	-7	17	-23
18768p1	75072p1	3519f1	29325f1	57477f1	19941g1	26979l1

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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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