Cremona's table of elliptic curves

338 = 2 · 13²

Field	Data	Notes
Atkin-Lehner	2- 13+	Signs for the Atkin-Lehner involutions
Class	338c	Isogeny class
Conductor	338	Conductor
∏ cp	18	Product of Tamagawa factors cp
Δ	-32127240704 = -1 · 29 · 137	Discriminant
Eigenvalues	2-  1  3  1 -6 13+ -3 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-77659,-8336303]	[a1,a2,a3,a4,a6]
j	-10730978619193/6656	j-invariant
L	2.573914226694	L(r)(E,1)/r!
Ω	0.14299523481633	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	2704g3 10816i3 3042f3 8450c3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 338c3

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	3	1	-6	+	-3	-2	0	6	4	7	0	-1	-3	0	6	8	-14	3	-2	8	-12	6	10

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Quadratic twists for elliptic curve 338c3

-4	8	-3	5	-7	-11	13	17	-19
2704g3	10816i3	3042f3	8450c3	16562bm3	40898i3	26a2	97682m3	122018l3

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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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