Cremona's table of elliptic curves

1656 = 2³ · 3² · 23

Field	Data	Notes
Atkin-Lehner	2+ 3- 23+	Signs for the Atkin-Lehner involutions
Class	1656a	Isogeny class
Conductor	1656	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-9124527356928 = -1 · 210 · 318 · 23	Discriminant
Eigenvalues	2+ 3- -2 -4  4 -2  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,2229,139574]	[a1,a2,a3,a4,a6]
j	1640689628/12223143	j-invariant
L	1.0643355221662	L(r)(E,1)/r!
Ω	0.53216776108309	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3312g4 13248h4 552d4 41400cb3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1656a4

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

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Quadratic twists for elliptic curve 1656a4

-4	8	-3	5	-7	-23
3312g4	13248h4	552d4	41400cb3	81144q3	38088h3

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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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