Cremona's table of elliptic curves

9672 = 2³ · 3 · 13 · 31

Field	Data	Notes
Atkin-Lehner	2- 3+ 13+ 31+	Signs for the Atkin-Lehner involutions
Class	9672g	Isogeny class
Conductor	9672	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-30811342287667968 = -1 · 28 · 33 · 136 · 314	Discriminant
Eigenvalues	2- 3+  0 -4 -2 13+ -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-703628,-227098716]	[a1,a2,a3,a4,a6]
j	-150492100544118466000/120356805811203	j-invariant
L	0.32966503804269	L(r)(E,1)/r!
Ω	0.082416259510671	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	19344f2 77376u2 29016c2 125736e2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 9672g2

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

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Quadratic twists for elliptic curve 9672g2

-4	8	-3	13
19344f2	77376u2	29016c2	125736e2

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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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