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
deg	576	Modular degree for the optimal curve
Δ	10430532 = 22 · 36 · 72 · 73	Discriminant
Eigenvalues	2+ 3- -2 7-  0  0 -4  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-57,-56]	[a1,a2,a3,a4,a6]
Generators	[-4:12:1]	Generators of the group modulo torsion
j	19968681097/10430532	j-invariant
L	2.7418345589526	L(r)(E,1)/r!
Ω	1.8445682481526	Real period
R	0.24773950595201	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	24528h1 98112j1 9198k1 76650bu1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3066f1

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 3066f1

-4	8	-3	5	-7
24528h1	98112j1	9198k1	76650bu1	21462h1

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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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