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	1173c	Isogeny class
Conductor	1173	Conductor
∏ cp	35	Product of Tamagawa factors cp
deg	840	Modular degree for the optimal curve
Δ	239296796397 = 37 · 17 · 235	Discriminant
Eigenvalues	0 3- -2  1  2 -1 17+ -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-1689,12098]	[a1,a2,a3,a4,a6]
Generators	[-42:103:1]	Generators of the group modulo torsion
j	533174986473472/239296796397	j-invariant
L	2.4271699496563	L(r)(E,1)/r!
Ω	0.88833545313061	Real period
R	0.078064781274835	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	18768j1 75072m1 3519g1 29325i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1173c1

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	1	2	-1	+	-6	-	-9	2	-9	2	-2	4	-1	-4	-7	-4	-3	-8	-5	-11	5	-1

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Quadratic twists for elliptic curve 1173c1

-4	8	-3	5	-7	17	-23
18768j1	75072m1	3519g1	29325i1	57477i1	19941a1	26979n1

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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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