Cremona's table of elliptic curves

338 = 2 · 13²

Field	Data	Notes
Atkin-Lehner	2- 13+	Signs for the Atkin-Lehner involutions
Class	338b	Isogeny class
Conductor	338	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	156	Modular degree for the optimal curve
Δ	-3262922884 = -1 · 22 · 138	Discriminant
Eigenvalues	2-  0 -1  4  4 13+  3  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,137,2643]	[a1,a2,a3,a4,a6]
j	351/4	j-invariant
L	2.0867726373932	L(r)(E,1)/r!
Ω	1.0433863186966	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	2704e1 10816a1 3042b1 8450b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 338b1

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
-	0	-1	4	4	+	3	0	-4	-1	4	3	-9	-8	-8	-9	-4	7	4	-8	11	-4	0	-6	2

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Quadratic twists for elliptic curve 338b1

-4	8	-3	5	-7	-11	13	17	-19
2704e1	10816a1	3042b1	8450b1	16562be1	40898f1	338a1	97682k1	122018e1

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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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