Cremona's table of elliptic curves

11748 = 2² · 3 · 11 · 89

Field	Data	Notes
Atkin-Lehner	2- 3+ 11+ 89-	Signs for the Atkin-Lehner involutions
Class	11748a	Isogeny class
Conductor	11748	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	1089807637248 = 28 · 33 · 116 · 89	Discriminant
Eigenvalues	2- 3+  2  0 11+ -4 -4  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-12372,531432]	[a1,a2,a3,a4,a6]
Generators	[86:310:1]	Generators of the group modulo torsion
j	818160641289808/4257061083	j-invariant
L	4.241145885138	L(r)(E,1)/r!
Ω	0.87651700009647	Real period
R	3.2257567049821	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	46992p2 35244d2 129228e2	Quadratic twists by: -4 -3 -11

Hecke Eigenvalues for elliptic curve 11748a2

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	0	+	-4	-4	4	-4	6	0	6	2	4	-8	6	4	8	16	8	-2	-10	-10	-	-14

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Quadratic twists for elliptic curve 11748a2

-4	-3	-11
46992p2	35244d2	129228e2

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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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