Cremona's table of elliptic curves

646 = 2 · 17 · 19

Field	Data	Notes
Atkin-Lehner	2- 17+ 19+	Signs for the Atkin-Lehner involutions
Class	646b	Isogeny class
Conductor	646	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-1834455244 = -1 · 22 · 176 · 19	Discriminant
Eigenvalues	2-  2  2  0 -4  2 17+ 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,303,-229]	[a1,a2,a3,a4,a6]
j	3075827761007/1834455244	j-invariant
L	3.4666091771646	L(r)(E,1)/r!
Ω	0.86665229429115	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	5168i2 20672l2 5814g2 16150f2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 646b2

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

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Quadratic twists for elliptic curve 646b2

-4	8	-3	5	-7	-11	13	17	-19
5168i2	20672l2	5814g2	16150f2	31654y2	78166f2	109174d2	10982e2	12274f2

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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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