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	3066d	Isogeny class
Conductor	3066	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	240	Modular degree for the optimal curve
Δ	-6132 = -1 · 22 · 3 · 7 · 73	Discriminant
Eigenvalues	2+ 3+  0 7-  4  1  2 -5	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,5,1]	[a1,a2,a3,a4,a6]
Generators	[0:1:1]	Generators of the group modulo torsion
j	9938375/6132	j-invariant
L	2.3118104463388	L(r)(E,1)/r!
Ω	2.4530617621948	Real period
R	0.47120918069963	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	24528p1 98112bb1 9198m1 76650cp1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3066d1

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
+	+	0	-	4	1	2	-5	-9	-1	-10	3	-5	5	12	-9	1	8	-16	7	-	-10	15	-3	-8

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Quadratic twists for elliptic curve 3066d1

-4	8	-3	5	-7
24528p1	98112bb1	9198m1	76650cp1	21462n1

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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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