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	4	Product of Tamagawa factors cp
Δ	767637 = 310 · 13	Discriminant
Eigenvalues	-1 3- -2 -4 -4 13- -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-626,6180]	[a1,a2,a3,a4,a6]
Generators	[8:36:1]	Generators of the group modulo torsion
j	37159393753/1053	j-invariant
L	0.74611338874648	L(r)(E,1)/r!
Ω	2.6403251263283	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	1872q3 7488p4 39a2 2925f4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 117a4

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 117a4

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31
1872q3	7488p4	39a2	2925f4	5733g3	14157j3	1521d4	33813o4	42237b4	61893l4	98397y4	112437g4

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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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