Cremona's table of elliptic curves

3339 = 3² · 7 · 53

Field	Data	Notes
Atkin-Lehner	3- 7+ 53-	Signs for the Atkin-Lehner involutions
Class	3339b	Isogeny class
Conductor	3339	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	448	Modular degree for the optimal curve
Δ	-5679639 = -1 · 37 · 72 · 53	Discriminant
Eigenvalues	1 3-  2 7+  2  2 -8  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,9,112]	[a1,a2,a3,a4,a6]
Generators	[32:164:1]	Generators of the group modulo torsion
j	103823/7791	j-invariant
L	4.5121440885387	L(r)(E,1)/r!
Ω	1.835524034658	Real period
R	2.4582320924931	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	53424bw1 1113b1 83475bb1 23373g1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 3339b1

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
1	-	2	+	2	2	-8	0	0	-6	-8	2	2	0	0	-	4	-4	-10	0	-4	-10	-4	12	2

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Quadratic twists for elliptic curve 3339b1

-4	-3	5	-7
53424bw1	1113b1	83475bb1	23373g1

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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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