Cremona's table of elliptic curves

168 = 2³ · 3 · 7

Field	Data	Notes
Atkin-Lehner	2+ 3- 7+	Signs for the Atkin-Lehner involutions
Class	168a	Isogeny class
Conductor	168	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	580608 = 210 · 34 · 7	Discriminant
Eigenvalues	2+ 3-  2 7+  0 -2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-152,672]	[a1,a2,a3,a4,a6]
j	381775972/567	j-invariant
L	1.4512623704546	L(r)(E,1)/r!
Ω	2.9025247409092	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	336b3 1344b3 504f3 4200q3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 168a3

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

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Quadratic twists for elliptic curve 168a3

-4	8	-3	5	-7	-11	13	17	-19	-23
336b3	1344b3	504f3	4200q3	1176c3	20328bc3	28392bc4	48552i4	60648v4	88872r4

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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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