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	6	Product of Tamagawa factors cp
Δ	-84835994984 = -1 · 23 · 139	Discriminant
Eigenvalues	2-  1  3  1 -6 13+ -3 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-764,-16264]	[a1,a2,a3,a4,a6]
j	-10218313/17576	j-invariant
L	2.573914226694	L(r)(E,1)/r!
Ω	0.42898570444899	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	2704g2 10816i2 3042f2 8450c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 338c2

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 338c2

-4	8	-3	5	-7	-11	13	17	-19
2704g2	10816i2	3042f2	8450c2	16562bm2	40898i2	26a1	97682m2	122018l2

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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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