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	420	Product of Tamagawa factors cp
Δ	772449493500000 = 25 · 314 · 56 · 17 · 19	Discriminant
Eigenvalues	2- 3- 5-  0 -6 -2 17+ 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-49430,4008900]	[a1,a2,a3,a4,a6]
Generators	[-200:2530:1]	Generators of the group modulo torsion
j	13356605308524570721/772449493500000	j-invariant
L	7.8809329555368	L(r)(E,1)/r!
Ω	0.49676609224295	Real period
R	0.15109023242621	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	77520bm2 29070l2 48450i2	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 9690w2

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 9690w2

-4	-3	5
77520bm2	29070l2	48450i2

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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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