Cremona's table of elliptic curves

7968 = 2⁵ · 3 · 83

Field	Data	Notes
Atkin-Lehner	2- 3- 83-	Signs for the Atkin-Lehner involutions
Class	7968j	Isogeny class
Conductor	7968	Conductor
∏ cp	36	Product of Tamagawa factors cp
deg	27360	Modular degree for the optimal curve
Δ	-2057977637568 = -1 · 26 · 318 · 83	Discriminant
Eigenvalues	2- 3- -4  0  4  6  6  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-6450,-213156]	[a1,a2,a3,a4,a6]
j	-463756716835264/32155900587	j-invariant
L	2.3877243709163	L(r)(E,1)/r!
Ω	0.26530270787959	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	7968e1 15936r2 23904g1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 7968j1

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

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Quadratic twists for elliptic curve 7968j1

-4	8	-3
7968e1	15936r2	23904g1

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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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