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	1656f	Isogeny class
Conductor	1656	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	789792768 = 211 · 36 · 232	Discriminant
Eigenvalues	2- 3-  0  4 -6 -2 -6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-315,-1674]	[a1,a2,a3,a4,a6]
Generators	[30:126:1]	Generators of the group modulo torsion
j	2315250/529	j-invariant
L	2.9764254053573	L(r)(E,1)/r!
Ω	1.1518396659643	Real period
R	2.5840622556312	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	3312f2 13248f2 184c2 41400q2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1656f2

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
-	-	0	4	-6	-2	-6	-6	+	6	0	-8	-6	-2	8	8	-4	-4	2	8	6	12	-10	-10	-18

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Quadratic twists for elliptic curve 1656f2

-4	8	-3	5	-7	-23
3312f2	13248f2	184c2	41400q2	81144bq2	38088s2

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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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