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	646a	Isogeny class
Conductor	646	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-301302152 = -1 · 23 · 172 · 194	Discriminant
Eigenvalues	2+  0  4 -2  4  6 17+ 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-85,-867]	[a1,a2,a3,a4,a6]
j	-68367756969/301302152	j-invariant
L	1.4274356436688	L(r)(E,1)/r!
Ω	0.71371782183442	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	5168d2 20672d2 5814u2 16150u2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 646a2

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

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Quadratic twists for elliptic curve 646a2

-4	8	-3	5	-7	-11	13	17	-19
5168d2	20672d2	5814u2	16150u2	31654i2	78166m2	109174i2	10982a2	12274m2

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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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