Cremona's table of elliptic curves

5664 = 2⁵ · 3 · 59

Field	Data	Notes
Atkin-Lehner	2+ 3+ 59-	Signs for the Atkin-Lehner involutions
Class	5664b	Isogeny class
Conductor	5664	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-16040448 = -1 · 29 · 32 · 592	Discriminant
Eigenvalues	2+ 3+  0 -4  4 -4 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-48,-216]	[a1,a2,a3,a4,a6]
j	-24389000/31329	j-invariant
L	0.86378132747344	L(r)(E,1)/r!
Ω	0.86378132747344	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	5664d2 11328c2 16992g2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 5664b2

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

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Quadratic twists for elliptic curve 5664b2

-4	8	-3
5664d2	11328c2	16992g2

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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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