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	3168v	Isogeny class
Conductor	3168	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	-374134464 = -1 · 26 · 312 · 11	Discriminant
Eigenvalues	2- 3-  2 -2 11+ -2  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,51,-920]	[a1,a2,a3,a4,a6]
Generators	[20:90:1]	Generators of the group modulo torsion
j	314432/8019	j-invariant
L	3.5904649952829	L(r)(E,1)/r!
Ω	0.82020663452482	Real period
R	2.1887563719617	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	3168y1 6336cj2 1056f1 79200y1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3168v1

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	-2	+	-2	0	-2	0	8	-4	-6	4	-6	-8	6	-4	-6	-4	-8	-10	14	-8	-2	14

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Quadratic twists for elliptic curve 3168v1

-4	8	-3	5	-11
3168y1	6336cj2	1056f1	79200y1	34848u1

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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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