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	168b	Isogeny class
Conductor	168	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	24	Modular degree for the optimal curve
Δ	-1037232 = -1 · 24 · 33 · 74	Discriminant
Eigenvalues	2+ 3+  2 7-  0  6 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-7,52]	[a1,a2,a3,a4,a6]
j	-2725888/64827	j-invariant
L	1.1607546520288	L(r)(E,1)/r!
Ω	2.3215093040576	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	336c1 1344j1 504g1 4200x1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 168b1

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

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Quadratic twists for elliptic curve 168b1

-4	8	-3	5	-7	-11	13	17	-19	-23
336c1	1344j1	504g1	4200x1	1176e1	20328q1	28392q1	48552p1	60648bp1	88872c1

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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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