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	76608x	Isogeny class
Conductor	76608	Conductor
∏ cp	96	Product of Tamagawa factors cp
Δ	5947287104445087744 = 217 · 39 · 72 · 196	Discriminant
Eigenvalues	2+ 3+ -2 7-  6  0  4 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-472716,-43387920]	[a1,a2,a3,a4,a6]
Generators	[-123:3591:1]	Generators of the group modulo torsion
j	4528177054182/2305248169	j-invariant
L	6.6729249876833	L(r)(E,1)/r!
Ω	0.19220537199623	Real period
R	1.4465700841605	Regulator
r	1	Rank of the group of rational points
S	1.0000000000316	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	76608cx2 9576d2 76608w2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 76608x2

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	-	6	0	4	-	-4	-2	-2	0	10	4	-4	-14	0	2	-12	0	-2	10	-6	10	-2

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Quadratic twists for elliptic curve 76608x2

-4	8	-3
76608cx2	9576d2	76608w2

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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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