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	494c	Isogeny class
Conductor	494	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	152	Modular degree for the optimal curve
Δ	-9386 = -1 · 2 · 13 · 192	Discriminant
Eigenvalues	2+  3 -3  3  0 13+  5 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-61,-169]	[a1,a2,a3,a4,a6]
j	-25334470953/9386	j-invariant
L	1.7069634647305	L(r)(E,1)/r!
Ω	0.85348173236523	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	3952f1 15808k1 4446s1 12350u1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 494c1

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	-3	3	0	+	5	-	6	-8	8	-5	-10	7	-1	-10	6	-6	-4	-5	8	12	-8	0	-2

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Quadratic twists for elliptic curve 494c1

-4	8	-3	5	-7	-11	13	-19
3952f1	15808k1	4446s1	12350u1	24206g1	59774w1	6422h1	9386m1

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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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