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	1564a	Isogeny class
Conductor	1564	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	624	Modular degree for the optimal curve
Δ	-30735728 = -1 · 24 · 174 · 23	Discriminant
Eigenvalues	2- -3  0  2  4 -1 17+  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-445,-3623]	[a1,a2,a3,a4,a6]
j	-609093216000/1920983	j-invariant
L	1.0392679487841	L(r)(E,1)/r!
Ω	0.51963397439205	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	6256g1 25024d1 14076g1 39100j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1564a1

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	0	2	4	-1	+	2	+	1	1	-4	-1	12	-7	6	12	6	0	5	-3	10	-6	0	-2

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Quadratic twists for elliptic curve 1564a1

-4	8	-3	5	-7	17	-23
6256g1	25024d1	14076g1	39100j1	76636e1	26588d1	35972f1

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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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