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	2	Product of Tamagawa factors cp
deg	34	Modular degree for the optimal curve
Δ	-3952 = -1 · 24 · 13 · 19	Discriminant
Eigenvalues	2+  0  2  4  4 13+  2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,4,0]	[a1,a2,a3,a4,a6]
j	6128487/3952	j-invariant
L	1.3738178096809	L(r)(E,1)/r!
Ω	2.7476356193618	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	3952d1 15808h1 4446q1 12350s1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 494b1

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 494b1

-4	8	-3	5	-7	-11	13	-19
3952d1	15808h1	4446q1	12350s1	24206e1	59774q1	6422e1	9386h1

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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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