Cremona's table of elliptic curves

13776 = 2⁴ · 3 · 7 · 41

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 41+	Signs for the Atkin-Lehner involutions
Class	13776o	Isogeny class
Conductor	13776	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	1209643008 = 212 · 3 · 74 · 41	Discriminant
Eigenvalues	2- 3-  2 7+  0  2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-10512,411348]	[a1,a2,a3,a4,a6]
Generators	[5268:65170:27]	Generators of the group modulo torsion
j	31366144171153/295323	j-invariant
L	6.4898915282858	L(r)(E,1)/r!
Ω	1.3868155319211	Real period
R	4.6797078478748	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	861a3 55104bt4 41328bo4 96432bu4	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 13776o4

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	2	-2	4	-8	-6	-4	6	+	-12	0	-6	-12	14	4	-4	2	-8	-4	-10	6

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Quadratic twists for elliptic curve 13776o4

-4	8	-3	-7
861a3	55104bt4	41328bo4	96432bu4

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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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