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	76608dz	Isogeny class
Conductor	76608	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	392249512230912 = 216 · 38 · 7 · 194	Discriminant
Eigenvalues	2- 3- -2 7+  4 -2 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-52716,-4560176]	[a1,a2,a3,a4,a6]
Generators	[-144:212:1]	Generators of the group modulo torsion
j	339112345828/8210223	j-invariant
L	5.0967780010534	L(r)(E,1)/r!
Ω	0.31554021720886	Real period
R	4.0381366004791	Regulator
r	1	Rank of the group of rational points
S	1.0000000001798	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	76608cp3 19152r3 25536ct3	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 76608dz3

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

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Quadratic twists for elliptic curve 76608dz3

-4	8	-3
76608cp3	19152r3	25536ct3

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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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