Cremona's table of elliptic curves

9690 = 2 · 3 · 5 · 17 · 19

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 17+ 19-	Signs for the Atkin-Lehner involutions
Class	9690w	Isogeny class
Conductor	9690	Conductor
∏ cp	840	Product of Tamagawa factors cp
deg	26880	Modular degree for the optimal curve
Δ	-29205442944000 = -1 · 210 · 37 · 53 · 172 · 192	Discriminant
Eigenvalues	2- 3- 5-  0 -6 -2 17+ 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,2250,256932]	[a1,a2,a3,a4,a6]
Generators	[84:-1062:1]	Generators of the group modulo torsion
j	1259677008323999/29205442944000	j-invariant
L	7.8809329555368	L(r)(E,1)/r!
Ω	0.49676609224295	Real period
R	0.075545116213103	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	77520bm1 29070l1 48450i1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 9690w1

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
-	-	-	0	-6	-2	+	-	0	-4	-4	0	-6	-4	4	10	-6	6	-14	6	-12	12	-4	-16	-6

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Quadratic twists for elliptic curve 9690w1

-4	-3	5
77520bm1	29070l1	48450i1

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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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