Cremona's table of elliptic curves

8464 = 2⁴ · 23²

Field	Data	Notes
Atkin-Lehner	2- 23-	Signs for the Atkin-Lehner involutions
Class	8464o	Isogeny class
Conductor	8464	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	-20528754925502464 = -1 · 218 · 238	Discriminant
Eigenvalues	2-  2  3 -2 -6 -1  6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-969304,367702512]	[a1,a2,a3,a4,a6]
Generators	[3882:26979:8]	Generators of the group modulo torsion
j	-313994137/64	j-invariant
L	6.4361194169991	L(r)(E,1)/r!
Ω	0.37307277322953	Real period
R	2.8752743337823	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	1058b2 33856bo2 76176ci2 8464p2	Quadratic twists by: -4 8 -3 -23

Hecke Eigenvalues for elliptic curve 8464o2

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	3	-2	-6	-1	6	-2	-	-9	4	2	-9	4	-6	3	-6	-1	-8	-6	11	-8	0	-9	-1

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Quadratic twists for elliptic curve 8464o2

-4	8	-3	-23
1058b2	33856bo2	76176ci2	8464p2

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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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