Cremona's table of elliptic curves

5688 = 2³ · 3² · 79

Field	Data	Notes
Atkin-Lehner	2- 3+ 79-	Signs for the Atkin-Lehner involutions
Class	5688d	Isogeny class
Conductor	5688	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-31447450368 = -1 · 28 · 39 · 792	Discriminant
Eigenvalues	2- 3+ -4  4 -2 -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-567,-9990]	[a1,a2,a3,a4,a6]
Generators	[57:378:1]	Generators of the group modulo torsion
j	-4000752/6241	j-invariant
L	3.2939257843559	L(r)(E,1)/r!
Ω	0.46376955251534	Real period
R	1.7756263679292	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	11376b2 45504h2 5688a2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 5688d2

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

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Quadratic twists for elliptic curve 5688d2

-4	8	-3
11376b2	45504h2	5688a2

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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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