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	3168r	Isogeny class
Conductor	3168	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-1672704 = -1 · 29 · 33 · 112	Discriminant
Eigenvalues	2- 3+  2 -4 11-  4 -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,21,50]	[a1,a2,a3,a4,a6]
Generators	[2:10:1]	Generators of the group modulo torsion
j	74088/121	j-invariant
L	3.5224790383592	L(r)(E,1)/r!
Ω	1.816537453582	Real period
R	1.9391172097296	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3168n2 6336bm2 3168d2 79200k2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3168r2

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

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Quadratic twists for elliptic curve 3168r2

-4	8	-3	5	-11
3168n2	6336bm2	3168d2	79200k2	34848e2

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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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