Cremona's table of elliptic curves

9968 = 2⁴ · 7 · 89

Field	Data	Notes
Atkin-Lehner	2- 7- 89-	Signs for the Atkin-Lehner involutions
Class	9968q	Isogeny class
Conductor	9968	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	7680	Modular degree for the optimal curve
Δ	-285802496 = -1 · 216 · 72 · 89	Discriminant
Eigenvalues	2-  3 -3 7-  0 -6 -3  7	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-19,-814]	[a1,a2,a3,a4,a6]
j	-185193/69776	j-invariant
L	3.1085248786267	L(r)(E,1)/r!
Ω	0.77713121965667	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1246c1 39872bo1 89712bd1 69776w1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 9968q1

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
-	3	-3	-	0	-6	-3	7	5	-2	7	-12	6	7	2	5	-4	-6	-2	-2	13	8	12	-	3

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Quadratic twists for elliptic curve 9968q1

-4	8	-3	-7
1246c1	39872bo1	89712bd1	69776w1

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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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