Cremona's table of elliptic curves

3168 = 2⁵ · 3² · 11

Field	Data	Notes
Atkin-Lehner	2- 3- 11-	Signs for the Atkin-Lehner involutions
Class	3168z	Isogeny class
Conductor	3168	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	155537541908508672 = 212 · 311 · 118	Discriminant
Eigenvalues	2- 3- -2  4 11- -2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-187356,-24784544]	[a1,a2,a3,a4,a6]
j	243578556889408/52089208083	j-invariant
L	1.8636042950747	L(r)(E,1)/r!
Ω	0.23295053688434	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	3168i2 6336n1 1056d2 79200bv3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3168z3

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	4	-	-2	-2	4	0	6	4	-2	6	-4	8	6	-12	-10	4	0	10	12	-12	-10	18

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Quadratic twists for elliptic curve 3168z3

-4	8	-3	5	-11
3168i2	6336n1	1056d2	79200bv3	34848bb3

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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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