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	3339g	Isogeny class
Conductor	3339	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	1920	Modular degree for the optimal curve
Δ	-13252491 = -1 · 36 · 73 · 53	Discriminant
Eigenvalues	-2 3- -3 7- -3 -6 -6 -5	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-279,1802]	[a1,a2,a3,a4,a6]
Generators	[45:-284:1] [-12:58:1]	Generators of the group modulo torsion
j	-3294646272/18179	j-invariant
L	2.1034272932555	L(r)(E,1)/r!
Ω	2.2510133113553	Real period
R	0.077869645144684	Regulator
r	2	Rank of the group of rational points
S	1.0000000000006	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	53424bi1 371b1 83475r1 23373p1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 3339g1

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	-	-3	-	-3	-6	-6	-5	-4	-5	-11	5	9	4	-4	-	2	1	-12	-4	-10	-10	-5	-16	10

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Quadratic twists for elliptic curve 3339g1

-4	-3	5	-7
53424bi1	371b1	83475r1	23373p1

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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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