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	1173d	Isogeny class
Conductor	1173	Conductor
∏ cp	77	Product of Tamagawa factors cp
deg	3696	Modular degree for the optimal curve
Δ	-1671876092836413 = -1 · 311 · 177 · 23	Discriminant
Eigenvalues	1 3-  0 -2 -3  1 17- -5	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,15139,-1830679]	[a1,a2,a3,a4,a6]
Generators	[123:1315:1]	Generators of the group modulo torsion
j	383757181824152375/1671876092836413	j-invariant
L	3.3898949912801	L(r)(E,1)/r!
Ω	0.23911882446997	Real period
R	0.18411185473979	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	18768q1 75072q1 3519e1 29325d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1173d1

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	-	0	-2	-3	1	-	-5	+	-5	-3	2	-5	-4	-7	9	-5	1	11	-6	14	-4	12	5	-3

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Quadratic twists for elliptic curve 1173d1

-4	8	-3	5	-7	17	-23
18768q1	75072q1	3519e1	29325d1	57477a1	19941d1	26979i1

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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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