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	3366k	Isogeny class
Conductor	3366	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	8960	Modular degree for the optimal curve
Δ	542744395776 = 214 · 311 · 11 · 17	Discriminant
Eigenvalues	2+ 3-  2 -4 11- -4 17- -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-8136,-278208]	[a1,a2,a3,a4,a6]
j	81706955619457/744505344	j-invariant
L	1.005919273863	L(r)(E,1)/r!
Ω	0.50295963693151	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	26928bj1 107712bs1 1122i1 84150fr1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3366k1

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

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Quadratic twists for elliptic curve 3366k1

-4	8	-3	5	-11	17
26928bj1	107712bs1	1122i1	84150fr1	37026bd1	57222k1

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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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