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	1173a	Isogeny class
Conductor	1173	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	128	Modular degree for the optimal curve
Δ	-1173 = -1 · 3 · 17 · 23	Discriminant
Eigenvalues	-1 3+ -4 -2  5  1 17+ -1	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-20,26]	[a1,a2,a3,a4,a6]
Generators	[2:-1:1]	Generators of the group modulo torsion
j	-887503681/1173	j-invariant
L	1.1077932769436	L(r)(E,1)/r!
Ω	4.8624591119561	Real period
R	0.22782572592122	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	18768y1 75072bh1 3519h1 29325s1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1173a1

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	+	-4	-2	5	1	+	-1	+	-1	11	6	-9	-4	3	-9	-15	11	7	2	-10	12	-12	3	-1

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Quadratic twists for elliptic curve 1173a1

-4	8	-3	5	-7	17	-23
18768y1	75072bh1	3519h1	29325s1	57477q1	19941l1	26979f1

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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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