Cremona's table of elliptic curves

1196 = 2² · 13 · 23

Field	Data	Notes
Atkin-Lehner	2- 13+ 23-	Signs for the Atkin-Lehner involutions
Class	1196a	Isogeny class
Conductor	1196	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	-653665782016 = -1 · 28 · 136 · 232	Discriminant
Eigenvalues	2-  0 -2  2  2 13+ -2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,2089,12750]	[a1,a2,a3,a4,a6]
Generators	[3:138:1]	Generators of the group modulo torsion
j	3938211778608/2553381961	j-invariant
L	2.433909008603	L(r)(E,1)/r!
Ω	0.56826854004879	Real period
R	1.4276753782605	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	4784b2 19136m2 10764f2 29900d2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1196a2

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	2	2	+	-2	-2	-	2	-6	-10	-6	4	6	-10	6	-2	-10	-6	-6	-12	-10	6	6

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Quadratic twists for elliptic curve 1196a2

-4	8	-3	5	-7	13	-23
4784b2	19136m2	10764f2	29900d2	58604k2	15548b2	27508a2

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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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