Cremona's table of elliptic curves

6608 = 2⁴ · 7 · 59

Field	Data	Notes
Atkin-Lehner	2+ 7+ 59-	Signs for the Atkin-Lehner involutions
Class	6608b	Isogeny class
Conductor	6608	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	40800	Modular degree for the optimal curve
Δ	-7069296338944 = -1 · 211 · 75 · 593	Discriminant
Eigenvalues	2+ -2 -1 7+ -6  6  4  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-244776,-46694252]	[a1,a2,a3,a4,a6]
j	-791957789108586578/3451804853	j-invariant
L	0.64391469975325	L(r)(E,1)/r!
Ω	0.10731911662554	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3304a1 26432e1 59472j1 46256l1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 6608b1

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	-1	+	-6	6	4	2	1	2	2	-3	-2	-8	-8	-10	-	-14	-12	12	10	-10	9	1	1

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Quadratic twists for elliptic curve 6608b1

-4	8	-3	-7
3304a1	26432e1	59472j1	46256l1

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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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