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	52416t	Isogeny class
Conductor	52416	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	-107744407400448 = -1 · 212 · 33 · 78 · 132	Discriminant
Eigenvalues	2+ 3+ -2 7- -2 13+ -8  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-124836,16984224]	[a1,a2,a3,a4,a6]
Generators	[-44:4732:1] [40:3472:1]	Generators of the group modulo torsion
j	-1945447581589056/974251369	j-invariant
L	8.8678574096635	L(r)(E,1)/r!
Ω	0.58642583167264	Real period
R	0.94511711143941	Regulator
r	2	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	52416j2 26208e1 52416s2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 52416t2

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

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Quadratic twists for elliptic curve 52416t2

-4	8	-3
52416j2	26208e1	52416s2

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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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