Cremona's table of elliptic curves

494 = 2 · 13 · 19

Field	Data	Notes
Atkin-Lehner	2+ 13+ 19-	Signs for the Atkin-Lehner involutions
Class	494b	Isogeny class
Conductor	494	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	3388346 = 2 · 13 · 194	Discriminant
Eigenvalues	2+  0  2  4  4 13+  2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-146,-638]	[a1,a2,a3,a4,a6]
j	345505073913/3388346	j-invariant
L	1.3738178096809	L(r)(E,1)/r!
Ω	1.3738178096809	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3952d4 15808h3 4446q4 12350s3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 494b3

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	2	4	4	+	2	-	-8	2	0	10	-2	12	4	-6	-12	14	-12	8	2	-16	-12	6	-2

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Quadratic twists for elliptic curve 494b3

-4	8	-3	5	-7	-11	13	-19
3952d4	15808h3	4446q4	12350s3	24206e3	59774q3	6422e3	9386h4

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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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