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	13776p	Isogeny class
Conductor	13776	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	95279778004992 = 215 · 3 · 73 · 414	Discriminant
Eigenvalues	2- 3- -2 7+  4  2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-703024,-227117740]	[a1,a2,a3,a4,a6]
Generators	[486910412:32773743786:103823]	Generators of the group modulo torsion
j	9381555148655972017/23261664552	j-invariant
L	5.1304728146585	L(r)(E,1)/r!
Ω	0.16487584334094	Real period
R	15.558594608821	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	1722m4 55104bs4 41328bn4 96432br4	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 13776p3

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	+	4	2	-2	-4	8	-2	-4	-10	+	-4	8	-2	0	-6	8	12	-14	8	-16	6	-2

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Quadratic twists for elliptic curve 13776p3

-4	8	-3	-7
1722m4	55104bs4	41328bn4	96432br4

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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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