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	2	Product of Tamagawa factors cp
deg	112	Modular degree for the optimal curve
Δ	-125497034 = -1 · 2 · 137	Discriminant
Eigenvalues	2-  1  3  1 -6 13+ -3 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,81,467]	[a1,a2,a3,a4,a6]
j	12167/26	j-invariant
L	2.573914226694	L(r)(E,1)/r!
Ω	1.286957113347	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	2704g1 10816i1 3042f1 8450c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 338c1

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 338c1

-4	8	-3	5	-7	-11	13	17	-19
2704g1	10816i1	3042f1	8450c1	16562bm1	40898i1	26a3	97682m1	122018l1

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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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