Cremona's table of elliptic curves

3393 = 3² · 13 · 29

Field	Data	Notes
Atkin-Lehner	3- 13- 29+	Signs for the Atkin-Lehner involutions
Class	3393g	Isogeny class
Conductor	3393	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	603808101 = 36 · 134 · 29	Discriminant
Eigenvalues	-1 3-  2  0  4 13- -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1424,20998]	[a1,a2,a3,a4,a6]
Generators	[26:19:1]	Generators of the group modulo torsion
j	437764156857/828269	j-invariant
L	2.6137246175405	L(r)(E,1)/r!
Ω	1.6300975104656	Real period
R	0.80170805757315	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	54288bo4 377a3 84825m4 44109s4	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 3393g3

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	0	4	-	-2	-4	-8	+	-8	2	10	-8	-8	-6	-12	6	12	16	-10	-12	12	10	14

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Quadratic twists for elliptic curve 3393g3

-4	-3	5	13	29
54288bo4	377a3	84825m4	44109s4	98397x4

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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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