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	9690p	Isogeny class
Conductor	9690	Conductor
∏ cp	648	Product of Tamagawa factors cp
deg	248832	Modular degree for the optimal curve
Δ	-1372088137570776000 = -1 · 26 · 39 · 53 · 176 · 192	Discriminant
Eigenvalues	2+ 3- 5- -4 -6  2 17- 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-197668,-65745694]	[a1,a2,a3,a4,a6]
Generators	[580:3557:1]	Generators of the group modulo torsion
j	-854141175043560052921/1372088137570776000	j-invariant
L	3.4675524638075	L(r)(E,1)/r!
Ω	0.10722009978539	Real period
R	1.796694872794	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	77520by1 29070be1 48450be1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 9690p1

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
+	-	-	-4	-6	2	-	-	0	0	8	8	6	-4	-12	6	-6	2	2	-6	8	-16	12	-12	-10

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Quadratic twists for elliptic curve 9690p1

-4	-3	5
77520by1	29070be1	48450be1

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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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