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
deg	8	Modular degree for the optimal curve
Δ	-28431 = -1 · 37 · 13	Discriminant
Eigenvalues	-1 3- -2 -4 -4 13- -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,4,6]	[a1,a2,a3,a4,a6]
Generators	[0:2:1]	Generators of the group modulo torsion
j	12167/39	j-invariant
L	0.74611338874648	L(r)(E,1)/r!
Ω	2.6403251263283	Real period
R	1.1303356261796	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	1872q1 7488p1 39a4 2925f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 117a1

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 117a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31
1872q1	7488p1	39a4	2925f1	5733g1	14157j1	1521d1	33813o1	42237b1	61893l1	98397y1	112437g1

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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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