Cremona's table of elliptic curves

3066 = 2 · 3 · 7 · 73

Field	Data	Notes
Atkin-Lehner	2+ 3- 7- 73+	Signs for the Atkin-Lehner involutions
Class	3066f	Isogeny class
Conductor	3066	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	-690926166 = -1 · 2 · 33 · 74 · 732	Discriminant
Eigenvalues	2+ 3- -2 7-  0  0 -4  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,213,-380]	[a1,a2,a3,a4,a6]
Generators	[14:66:1]	Generators of the group modulo torsion
j	1075945339223/690926166	j-invariant
L	2.7418345589526	L(r)(E,1)/r!
Ω	0.92228412407632	Real period
R	0.49547901190402	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	24528h2 98112j2 9198k2 76650bu2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3066f2

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	0	-4	0	4	-6	4	-6	-6	6	2	-6	0	-6	-4	-12	+	16	4	6	-2

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Quadratic twists for elliptic curve 3066f2

-4	8	-3	5	-7
24528h2	98112j2	9198k2	76650bu2	21462h2

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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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