Cremona's table of elliptic curves

8464 = 2⁴ · 23²

Field	Data	Notes
Atkin-Lehner	2- 23-	Signs for the Atkin-Lehner involutions
Class	8464k	Isogeny class
Conductor	8464	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	13248	Modular degree for the optimal curve
Δ	-20047612231936 = -1 · 28 · 238	Discriminant
Eigenvalues	2-  0  1 -2  4  1 -2  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-12167,559682]	[a1,a2,a3,a4,a6]
Generators	[1058:8993:8]	Generators of the group modulo torsion
j	-9936	j-invariant
L	4.3026752580393	L(r)(E,1)/r!
Ω	0.66717611052584	Real period
R	2.1496949057164	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	2116a1 33856z1 76176bz1 8464l1	Quadratic twists by: -4 8 -3 -23

Hecke Eigenvalues for elliptic curve 8464k1

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	1	-2	4	1	-2	2	-	5	6	-10	-9	-10	12	5	-6	1	-8	6	-9	-12	10	15	15

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Quadratic twists for elliptic curve 8464k1

-4	8	-3	-23
2116a1	33856z1	76176bz1	8464l1

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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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