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	494d	Isogeny class
Conductor	494	Conductor
∏ cp	78	Product of Tamagawa factors cp
deg	312	Modular degree for the optimal curve
Δ	-6497214464 = -1 · 213 · 133 · 192	Discriminant
Eigenvalues	2- -1 -1 -3 -4 13- -3 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-1001,12375]	[a1,a2,a3,a4,a6]
Generators	[45:224:1]	Generators of the group modulo torsion
j	-110931033861649/6497214464	j-invariant
L	2.1566805189123	L(r)(E,1)/r!
Ω	1.3176510859324	Real period
R	0.020984121318353	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	3952j1 15808d1 4446g1 12350a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 494d1

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

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Quadratic twists for elliptic curve 494d1

-4	8	-3	5	-7	-11	13	-19
3952j1	15808d1	4446g1	12350a1	24206l1	59774c1	6422a1	9386e1

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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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