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	3393c	Isogeny class
Conductor	3393	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	14016	Modular degree for the optimal curve
Δ	-7420491 = -1 · 39 · 13 · 29	Discriminant
Eigenvalues	-2 3+  1  0  2 13- -7  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-317547,-68874766]	[a1,a2,a3,a4,a6]
Generators	[454995:27099932:125]	Generators of the group modulo torsion
j	-179910479913725952/377	j-invariant
L	1.9822629237226	L(r)(E,1)/r!
Ω	0.10055821496709	Real period
R	9.8562953030306	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	54288ba1 3393a1 84825d1 44109k1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 3393c1

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	+	1	0	2	-	-7	8	-4	-	1	-1	-4	-2	-10	-12	-9	6	-6	8	14	6	0	-4	-1

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Quadratic twists for elliptic curve 3393c1

-4	-3	5	13	29
54288ba1	3393a1	84825d1	44109k1	98397i1

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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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