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	9672i	Isogeny class
Conductor	9672	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	1496761344 = 210 · 32 · 132 · 312	Discriminant
Eigenvalues	2- 3- -2  0 -4 13+ -2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-424,-2944]	[a1,a2,a3,a4,a6]
j	8251733668/1461681	j-invariant
L	1.064671849859	L(r)(E,1)/r!
Ω	1.064671849859	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	19344a2 77376k2 29016e2 125736l2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 9672i2

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	0	-4	+	-2	-8	0	2	-	-6	-6	-4	0	10	12	10	16	0	14	12	4	-6	2

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Quadratic twists for elliptic curve 9672i2

-4	8	-3	13
19344a2	77376k2	29016e2	125736l2

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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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