Cremona's table of elliptic curves

5696 = 2⁶ · 89

Field	Data	Notes
Atkin-Lehner	2+ 89-	Signs for the Atkin-Lehner involutions
Class	5696d	Isogeny class
Conductor	5696	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	364544 = 212 · 89	Discriminant
Eigenvalues	2+  0 -2 -2 -4 -4 -2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-116,480]	[a1,a2,a3,a4,a6]
Generators	[-12:12:1] [2:16:1]	Generators of the group modulo torsion
j	42144192/89	j-invariant
L	4.3026708991367	L(r)(E,1)/r!
Ω	3.0256324292404	Real period
R	1.4220732358478	Regulator
r	2	Rank of the group of rational points
S	1.0000000000002	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	5696c1 2848a1 51264j1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 5696d1

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

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Quadratic twists for elliptic curve 5696d1

-4	8	-3
5696c1	2848a1	51264j1

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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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