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	2	Product of Tamagawa factors cp
deg	8	Modular degree for the optimal curve
Δ	336 = 24 · 3 · 7	Discriminant
Eigenvalues	2+ 3-  2 7+  0 -2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-7,-10]	[a1,a2,a3,a4,a6]
j	2725888/21	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	2	Number of elements in the torsion subgroup
Twists	336b1 1344b1 504f1 4200q1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 168a1

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 168a1

-4	8	-3	5	-7	-11	13	17	-19	-23
336b1	1344b1	504f1	4200q1	1176c1	20328bc1	28392bc1	48552i1	60648v1	88872r1

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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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