Cremona's table of elliptic curves

9800 = 2³ · 5² · 7²

Field	Data	Notes
Atkin-Lehner	2+ 5+ 7-	Signs for the Atkin-Lehner involutions
Class	9800k	Isogeny class
Conductor	9800	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	9216	Modular degree for the optimal curve
Δ	-137200000000 = -1 · 210 · 58 · 73	Discriminant
Eigenvalues	2+ -2 5+ 7-  4 -2  0  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,992,13488]	[a1,a2,a3,a4,a6]
j	19652/25	j-invariant
L	1.3919059000083	L(r)(E,1)/r!
Ω	0.69595295000417	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	19600u1 78400cn1 88200gz1 1960o1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 9800k1

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	+	-	4	-2	0	2	4	10	4	2	-12	4	-4	-2	10	6	-4	-12	4	-4	-14	8	8

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Quadratic twists for elliptic curve 9800k1

-4	8	-3	5	-7
19600u1	78400cn1	88200gz1	1960o1	9800i1

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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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