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	9680a	Isogeny class
Conductor	9680	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	8064	Modular degree for the optimal curve
Δ	-212960000000 = -1 · 211 · 57 · 113	Discriminant
Eigenvalues	2+ -1 5+  3 11+  4 -3 -3	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,224,-22240]	[a1,a2,a3,a4,a6]
Generators	[26:22:1]	Generators of the group modulo torsion
j	453962/78125	j-invariant
L	3.6818873191629	L(r)(E,1)/r!
Ω	0.47142095907498	Real period
R	1.952547531185	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	4840d1 38720cr1 87120bu1 48400b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 9680a1

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	+	3	+	4	-3	-3	-4	1	5	-5	2	-8	10	11	0	-1	-4	-5	-10	-8	0	-15	-6

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Quadratic twists for elliptic curve 9680a1

-4	8	-3	5	-11
4840d1	38720cr1	87120bu1	48400b1	9680b1

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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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