Cremona's table of elliptic curves

76608 = 2⁶ · 3² · 7 · 19

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 19+	Signs for the Atkin-Lehner involutions
Class	76608dx	Isogeny class
Conductor	76608	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	7605946220544 = 216 · 38 · 72 · 192	Discriminant
Eigenvalues	2- 3- -2 7+  0  2 -6 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-38316,-2883760]	[a1,a2,a3,a4,a6]
Generators	[-112:52:1]	Generators of the group modulo torsion
j	130213720228/159201	j-invariant
L	4.2510872615915	L(r)(E,1)/r!
Ω	0.34126079381385	Real period
R	3.1142511379838	Regulator
r	1	Rank of the group of rational points
S	0.99999999991894	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	76608cn2 19152q2 25536br2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 76608dx2

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

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Quadratic twists for elliptic curve 76608dx2

-4	8	-3
76608cn2	19152q2	25536br2

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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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