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	9800t	Isogeny class
Conductor	9800	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	34272	Modular degree for the optimal curve
Δ	361568318720000 = 211 · 54 · 710	Discriminant
Eigenvalues	2+ -2 5- 7-  4  2  3  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-20008,584688]	[a1,a2,a3,a4,a6]
Generators	[-998:8597:8]	Generators of the group modulo torsion
j	2450	j-invariant
L	3.2878596571698	L(r)(E,1)/r!
Ω	0.48730914100869	Real period
R	6.7469689781813	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	19600bm1 78400fj1 88200io1 9800bj1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 9800t1

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	3	0	3	-6	-9	0	-5	-6	-9	-6	-8	-8	14	11	2	9	6	-11	11

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Quadratic twists for elliptic curve 9800t1

-4	8	-3	5	-7
19600bm1	78400fj1	88200io1	9800bj1	9800n1

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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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