Cremona's table of elliptic curves

117117 = 3² · 7 · 11 · 13²

Field	Data	Notes
Atkin-Lehner	3- 7+ 11+ 13+	Signs for the Atkin-Lehner involutions
Class	117117r	Isogeny class
Conductor	117117	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	307200	Modular degree for the optimal curve
Δ	5689808661537 = 37 · 72 · 11 · 136	Discriminant
Eigenvalues	-1 3- -2 7+ 11+ 13+ -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-51746,-4516248]	[a1,a2,a3,a4,a6]
Generators	[-132:99:1] [-130:96:1]	Generators of the group modulo torsion
j	4354703137/1617	j-invariant
L	6.0905332519406	L(r)(E,1)/r!
Ω	0.31654881523555	Real period
R	4.8101058682833	Regulator
r	2	Rank of the group of rational points
S	0.99999999948937	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	39039h1 693d1	Quadratic twists by: -3 13

Hecke Eigenvalues for elliptic curve 117117r1

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	+	+	+	-2	-4	0	2	-8	-6	10	-4	-8	-6	4	-10	12	0	-2	16	4	18	-2

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Quadratic twists for elliptic curve 117117r1

-3	13
39039h1	693d1

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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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