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	3366i	Isogeny class
Conductor	3366	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	27809892 = 22 · 37 · 11 · 172	Discriminant
Eigenvalues	2+ 3- -2 -2 11-  4 17+  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-108,-324]	[a1,a2,a3,a4,a6]
Generators	[-6:12:1]	Generators of the group modulo torsion
j	192100033/38148	j-invariant
L	2.1894372636346	L(r)(E,1)/r!
Ω	1.5008596954176	Real period
R	0.72939438320561	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	26928bd1 107712x1 1122j1 84150ga1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3366i1

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	-	4	+	2	-2	-2	-4	6	-6	2	0	12	14	6	-4	2	-8	-2	12	-6	-6

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Quadratic twists for elliptic curve 3366i1

-4	8	-3	5	-11	17
26928bd1	107712x1	1122j1	84150ga1	37026bl1	57222g1

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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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