Cremona's table of elliptic curves

116699 = 11 · 103²

Field	Data	Notes
Atkin-Lehner	11+ 103-	Signs for the Atkin-Lehner involutions
Class	116699a	Isogeny class
Conductor	116699	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-13134575261819 = -1 · 11 · 1036	Discriminant
Eigenvalues	-2  1 -1 -2 11+  4 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-82965916,290841510162]	[a1,a2,a3,a4,a6]
Generators	[-378:567581:1] [657270:-5367:125]	Generators of the group modulo torsion
j	-52893159101157376/11	j-invariant
L	6.2398922467273	L(r)(E,1)/r!
Ω	0.28748294482842	Real period
R	5.426315164078	Regulator
r	2	Rank of the group of rational points
S	0.99999999919587	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	11a2	Quadratic twists by: -103

Hecke Eigenvalues for elliptic curve 116699a3

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
-2	1	-1	-2	+	4	-2	0	-1	0	-7	-3	-8	6	-8	6	5	12	7	3	-4	-10	-6	-15	-7

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Quadratic twists for elliptic curve 116699a3

-103
11a2

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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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