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
deg	336	Modular degree for the optimal curve
Δ	-8031810176 = -1 · 27 · 137	Discriminant
Eigenvalues	2+ -3  1 -1  2 13+ -3 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-454,5812]	[a1,a2,a3,a4,a6]
Generators	[23:73:1]	Generators of the group modulo torsion
j	-2146689/1664	j-invariant
L	0.95305624304778	L(r)(E,1)/r!
Ω	1.2055736043538	Real period
R	0.19763543254554	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	2704j1 10816p1 3042k1 8450t1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 338f1

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 338f1

-4	8	-3	5	-7	-11	13	17	-19
2704j1	10816p1	3042k1	8450t1	16562r1	40898bx1	26b1	97682h1	122018bh1

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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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