Cremona's table of elliptic curves

9680 = 2⁴ · 5 · 11²

Field	Data	Notes
Atkin-Lehner	2- 5+ 11-	Signs for the Atkin-Lehner involutions
Class	9680r	Isogeny class
Conductor	9680	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	11520	Modular degree for the optimal curve
Δ	-3192778096640 = -1 · 215 · 5 · 117	Discriminant
Eigenvalues	2- -1 5+ -1 11- -2  3 -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1976,93040]	[a1,a2,a3,a4,a6]
Generators	[26:242:1]	Generators of the group modulo torsion
j	-117649/440	j-invariant
L	2.9245461219257	L(r)(E,1)/r!
Ω	0.69682920512918	Real period
R	0.52461673900844	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1210c1 38720df1 87120fu1 48400bt1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 9680r1

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
-	-1	+	-1	-	-2	3	-1	-6	9	-5	5	6	8	-6	9	-6	-5	-8	9	10	14	-6	-15	8

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Quadratic twists for elliptic curve 9680r1

-4	8	-3	5	-11
1210c1	38720df1	87120fu1	48400bt1	880f1

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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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