Cremona's table of elliptic curves

338 = 2 · 13²

Field	Data	Notes
Atkin-Lehner	2+ 13+	Signs for the Atkin-Lehner involutions
Class	338f	Isogeny class
Conductor	338	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-605750213184506 = -1 · 2 · 1313	Discriminant
Eigenvalues	2+ -3  1 -1  2 13+ -3 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-35944,-2868878]	[a1,a2,a3,a4,a6]
Generators	[10839:180227:27]	Generators of the group modulo torsion
j	-1064019559329/125497034	j-invariant
L	0.95305624304778	L(r)(E,1)/r!
Ω	0.17222480062196	Real period
R	1.3834480278188	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	2704j2 10816p2 3042k2 8450t2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 338f2

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
+	-3	1	-1	2	+	-3	-6	-4	2	-4	-3	0	-5	-13	12	10	-8	2	5	10	-4	0	-6	-14

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Quadratic twists for elliptic curve 338f2

-4	8	-3	5	-7	-11	13	17	-19
2704j2	10816p2	3042k2	8450t2	16562r2	40898bx2	26b2	97682h2	122018bh2

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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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