Cremona's table of elliptic curves

1564 = 2² · 17 · 23

Field	Data	Notes
Atkin-Lehner	2- 17- 23-	Signs for the Atkin-Lehner involutions
Class	1564b	Isogeny class
Conductor	1564	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	168	Modular degree for the optimal curve
Δ	-106352 = -1 · 24 · 172 · 23	Discriminant
Eigenvalues	2-  3  2  0  0  3 17- -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,11,-7]	[a1,a2,a3,a4,a6]
j	9199872/6647	j-invariant
L	3.7625952529045	L(r)(E,1)/r!
Ω	1.8812976264523	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6256j1 25024j1 14076c1 39100a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1564b1

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
-	3	2	0	0	3	-	-2	-	-9	-1	0	-7	-2	9	2	4	2	2	-5	3	-12	14	4	8

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Quadratic twists for elliptic curve 1564b1

-4	8	-3	5	-7	17	-23
6256j1	25024j1	14076c1	39100a1	76636c1	26588b1	35972c1

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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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