Cremona's table of elliptic curves

11592 = 2³ · 3² · 7 · 23

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 23+	Signs for the Atkin-Lehner involutions
Class	11592k	Isogeny class
Conductor	11592	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	43008	Modular degree for the optimal curve
Δ	-447101840489472 = -1 · 210 · 318 · 72 · 23	Discriminant
Eigenvalues	2- 3-  0 7+  2 -6  6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-14115,1204814]	[a1,a2,a3,a4,a6]
Generators	[-125:1008:1]	Generators of the group modulo torsion
j	-416618810500/598934007	j-invariant
L	4.3265198845438	L(r)(E,1)/r!
Ω	0.47519410791332	Real period
R	2.2761855694836	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	23184o1 92736ba1 3864a1 81144bm1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 11592k1

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

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Quadratic twists for elliptic curve 11592k1

-4	8	-3	-7
23184o1	92736ba1	3864a1	81144bm1

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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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