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
Δ	725407488 = 28 · 36 · 132 · 23	Discriminant
Eigenvalues	2- 3+  0  0 -4 13+  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-89428,10323256]	[a1,a2,a3,a4,a6]
j	308964909568786000/2833623	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	14352bb2 57408bn2 10764g2 89700v2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3588a2

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 3588a2

-4	8	-3	5	13	-23
14352bb2	57408bn2	10764g2	89700v2	46644a2	82524a2

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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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