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	52416eu	Isogeny class
Conductor	52416	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	210254500292788224 = 216 · 318 · 72 · 132	Discriminant
Eigenvalues	2- 3- -2 7+  4 13+  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-6368556,-6185955760]	[a1,a2,a3,a4,a6]
Generators	[137088925790:5192539384032:37595375]	Generators of the group modulo torsion
j	597914615076708388/4400862921	j-invariant
L	5.7322165320761	L(r)(E,1)/r!
Ω	0.09503629642706	Real period
R	15.079019142162	Regulator
r	1	Rank of the group of rational points
S	0.99999999999667	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	52416cp4 13104w3 17472br4	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 52416eu4

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

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Quadratic twists for elliptic curve 52416eu4

-4	8	-3
52416cp4	13104w3	17472br4

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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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