Cremona's table of elliptic curves

1139 = 17 · 67

Field	Data	Notes
Atkin-Lehner	17- 67-	Signs for the Atkin-Lehner involutions
Class	1139a	Isogeny class
Conductor	1139	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	84	Modular degree for the optimal curve
Δ	-1139 = -1 · 17 · 67	Discriminant
Eigenvalues	0  1  2 -4  3  0 17- -3	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-107,-464]	[a1,a2,a3,a4,a6]
Generators	[26:122:1]	Generators of the group modulo torsion
j	-136750071808/1139	j-invariant
L	2.5775442219336	L(r)(E,1)/r!
Ω	0.74162726501926	Real period
R	3.4755251640683	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	18224i1 72896e1 10251f1 28475b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1139a1

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	1	2	-4	3	0	-	-3	0	-8	-3	-6	-7	0	-8	-6	-3	3	-	2	4	15	5	9	-2

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Quadratic twists for elliptic curve 1139a1

-4	8	-3	5	-7	17	-67
18224i1	72896e1	10251f1	28475b1	55811f1	19363a1	76313a1

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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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