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	9800h	Isogeny class
Conductor	9800	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	9216	Modular degree for the optimal curve
Δ	-6860000000 = -1 · 28 · 57 · 73	Discriminant
Eigenvalues	2+ -1 5+ 7- -5 -7  3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3033,65437]	[a1,a2,a3,a4,a6]
Generators	[237:-3550:1] [-23:350:1]	Generators of the group modulo torsion
j	-2249728/5	j-invariant
L	4.9705324541258	L(r)(E,1)/r!
Ω	1.332735217397	Real period
R	0.11654913681564	Regulator
r	2	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	19600n1 78400bj1 88200hj1 1960j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 9800h1

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	+	-	-5	-7	3	-2	-8	-5	-10	-4	-6	-2	7	10	-10	-12	2	0	2	-7	-4	-8	-17

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Quadratic twists for elliptic curve 9800h1

-4	8	-3	5	-7
19600n1	78400bj1	88200hj1	1960j1	9800g1

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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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