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	3366f	Isogeny class
Conductor	3366	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	26174016 = 26 · 37 · 11 · 17	Discriminant
Eigenvalues	2+ 3-  2  0 11+ -4 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-81,157]	[a1,a2,a3,a4,a6]
Generators	[-6:23:1]	Generators of the group modulo torsion
j	81182737/35904	j-invariant
L	2.8524932899909	L(r)(E,1)/r!
Ω	1.902676268198	Real period
R	1.499200540664	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	26928bu1 107712cl1 1122f1 84150es1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3366f1

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	+	-4	-	-4	4	0	2	0	-6	-12	10	4	-4	-2	-12	-8	-10	8	-4	6	-2

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Quadratic twists for elliptic curve 3366f1

-4	8	-3	5	-11	17
26928bu1	107712cl1	1122f1	84150es1	37026bc1	57222v1

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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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