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	1656g	Isogeny class
Conductor	1656	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	1184689152 = 210 · 37 · 232	Discriminant
Eigenvalues	2- 3- -4  2  0  2  4 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-507,4070]	[a1,a2,a3,a4,a6]
Generators	[-13:92:1]	Generators of the group modulo torsion
j	19307236/1587	j-invariant
L	2.4837521314951	L(r)(E,1)/r!
Ω	1.5036932142477	Real period
R	0.82588393295962	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3312i2 13248k2 552c2 41400n2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1656g2

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
-	-	-4	2	0	2	4	-6	+	-10	4	-2	6	-6	-8	-8	4	-2	6	0	-14	-10	-16	0	-18

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Quadratic twists for elliptic curve 1656g2

-4	8	-3	5	-7	-23
3312i2	13248k2	552c2	41400n2	81144bv2	38088bd2

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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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