Cremona's table of elliptic curves

3366 = 2 · 3² · 11 · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 11- 17-	Signs for the Atkin-Lehner involutions
Class	3366q	Isogeny class
Conductor	3366	Conductor
∏ cp	120	Product of Tamagawa factors cp
Δ	6323027176224 = 25 · 38 · 116 · 17	Discriminant
Eigenvalues	2- 3- -2 -2 11-  0 17- -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-26861,1696821]	[a1,a2,a3,a4,a6]
Generators	[107:144:1]	Generators of the group modulo torsion
j	2940001530995593/8673562656	j-invariant
L	4.3875142039139	L(r)(E,1)/r!
Ω	0.75577934518852	Real period
R	0.19350948712063	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	26928bk2 107712bk2 1122a2 84150ch2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3366q2

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

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Quadratic twists for elliptic curve 3366q2

-4	8	-3	5	-11	17
26928bk2	107712bk2	1122a2	84150ch2	37026l2	57222bi2

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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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