Cremona's table of elliptic curves

52416 = 2⁶ · 3² · 7 · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 13-	Signs for the Atkin-Lehner involutions
Class	52416fl	Isogeny class
Conductor	52416	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	9782083584 = 214 · 38 · 7 · 13	Discriminant
Eigenvalues	2- 3- -2 7+  0 13- -4  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-17436,886160]	[a1,a2,a3,a4,a6]
Generators	[-32:1188:1] [28:648:1]	Generators of the group modulo torsion
j	49081386832/819	j-invariant
L	8.6351294129537	L(r)(E,1)/r!
Ω	1.1841895815126	Real period
R	3.6460080158481	Regulator
r	2	Rank of the group of rational points
S	0.9999999999996	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	52416de2 13104bs2 17472bv2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 52416fl2

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	0	-6	-6	-8	2	10	-12	6	-14	10	-14	-4	-12	-6	-8	-6	14	-18

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Quadratic twists for elliptic curve 52416fl2

-4	8	-3
52416de2	13104bs2	17472bv2

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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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