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	3393a	Isogeny class
Conductor	3393	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	4672	Modular degree for the optimal curve
Δ	-10179 = -1 · 33 · 13 · 29	Discriminant
Eigenvalues	2 3+ -1  0 -2 13-  7  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-35283,2550917]	[a1,a2,a3,a4,a6]
j	-179910479913725952/377	j-invariant
L	3.7476759883461	L(r)(E,1)/r!
Ω	1.8738379941731	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	54288x1 3393c1 84825a1 44109e1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 3393a1

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 3393a1

-4	-3	5	13	29
54288x1	3393c1	84825a1	44109e1	98397l1

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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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