Cremona's table of elliptic curves

9940 = 2² · 5 · 7 · 71

Field	Data	Notes
Atkin-Lehner	2- 5+ 7+ 71+	Signs for the Atkin-Lehner involutions
Class	9940a	Isogeny class
Conductor	9940	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	129600	Modular degree for the optimal curve
Δ	-970357846472224000 = -1 · 28 · 53 · 75 · 715	Discriminant
Eigenvalues	2- -2 5+ 7+ -5  2  4  1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,156844,-40869500]	[a1,a2,a3,a4,a6]
j	1666804662635700656/3790460337782125	j-invariant
L	0.43289752865456	L(r)(E,1)/r!
Ω	0.14429917621819	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	39760t1 89460k1 49700g1 69580p1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 9940a1

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	+	+	-5	2	4	1	-4	1	-4	-8	11	-5	-1	-6	-8	7	-8	+	-13	-12	6	-6	2

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Quadratic twists for elliptic curve 9940a1

-4	-3	5	-7
39760t1	89460k1	49700g1	69580p1

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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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