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	9800r	Isogeny class
Conductor	9800	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	57600	Modular degree for the optimal curve
Δ	-12358292143750000 = -1 · 24 · 58 · 711	Discriminant
Eigenvalues	2+ -2 5- 7-  1 -4  0 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-34708,5887713]	[a1,a2,a3,a4,a6]
Generators	[184:2401:1]	Generators of the group modulo torsion
j	-6288640/16807	j-invariant
L	2.7631434714218	L(r)(E,1)/r!
Ω	0.35346941158009	Real period
R	0.97715084420949	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	19600bj1 78400fg1 88200id1 9800bh1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 9800r1

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	-	-	1	-4	0	-6	3	-3	0	9	-2	9	6	6	-8	10	-1	-7	2	-9	-12	4	-16

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Quadratic twists for elliptic curve 9800r1

-4	8	-3	5	-7
19600bj1	78400fg1	88200id1	9800bh1	1400d1

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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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