Cremona's table of elliptic curves

3588 = 2² · 3 · 13 · 23

Field	Data	Notes
Atkin-Lehner	2- 3+ 13+ 23+	Signs for the Atkin-Lehner involutions
Class	3588a	Isogeny class
Conductor	3588	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	3456	Modular degree for the optimal curve
Δ	58475516112 = 24 · 312 · 13 · 232	Discriminant
Eigenvalues	2- 3+  0  0 -4 13+  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-5593,162454]	[a1,a2,a3,a4,a6]
j	1209527744512000/3654719757	j-invariant
L	1.1167088224081	L(r)(E,1)/r!
Ω	1.1167088224081	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	14352bb1 57408bn1 10764g1 89700v1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3588a1

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

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Quadratic twists for elliptic curve 3588a1

-4	8	-3	5	13	-23
14352bb1	57408bn1	10764g1	89700v1	46644a1	82524a1

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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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