Cremona's table of elliptic curves

117 = 3² · 13

Field	Data	Notes
Atkin-Lehner	3- 13-	Signs for the Atkin-Lehner involutions
Class	117a	Isogeny class
Conductor	117	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	62462907 = 37 · 134	Discriminant
Eigenvalues	-1 3- -2 -4 -4 13- -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-176,-768]	[a1,a2,a3,a4,a6]
Generators	[-6:9:1]	Generators of the group modulo torsion
j	822656953/85683	j-invariant
L	0.74611338874648	L(r)(E,1)/r!
Ω	1.3201625631642	Real period
R	0.28258390654489	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1872q4 7488p3 39a3 2925f3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 117a3

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	-	-2	-4	-4	-	-2	0	0	10	4	-2	-6	-12	0	-6	-12	-2	-8	0	2	8	-4	2	10

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Quadratic twists for elliptic curve 117a3

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31
1872q4	7488p3	39a3	2925f3	5733g4	14157j4	1521d3	33813o3	42237b3	61893l3	98397y3	112437g3

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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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