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	8	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	28377488 = 24 · 173 · 192	Discriminant
Eigenvalues	2-  2  2  0 -4  2 17+ 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-77,-77]	[a1,a2,a3,a4,a6]
j	50529889873/28377488	j-invariant
L	3.4666091771646	L(r)(E,1)/r!
Ω	1.7333045885823	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	5168i1 20672l1 5814g1 16150f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 646b1

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 646b1

-4	8	-3	5	-7	-11	13	17	-19
5168i1	20672l1	5814g1	16150f1	31654y1	78166f1	109174d1	10982e1	12274f1

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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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