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	1108809 = 38 · 132	Discriminant
Eigenvalues	-1 3- -2 -4 -4 13- -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-41,96]	[a1,a2,a3,a4,a6]
Generators	[-4:15:1]	Generators of the group modulo torsion
j	10218313/1521	j-invariant
L	0.74611338874648	L(r)(E,1)/r!
Ω	2.6403251263283	Real period
R	0.56516781308978	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	1872q2 7488p2 39a1 2925f2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 117a2

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 117a2

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31
1872q2	7488p2	39a1	2925f2	5733g2	14157j2	1521d2	33813o2	42237b2	61893l2	98397y2	112437g2

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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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