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	3588d	Isogeny class
Conductor	3588	Conductor
∏ cp	60	Product of Tamagawa factors cp
deg	24000	Modular degree for the optimal curve
Δ	98165896121331792 = 24 · 310 · 135 · 234	Discriminant
Eigenvalues	2- 3+  0  2  0 13- -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-166613,21455934]	[a1,a2,a3,a4,a6]
Generators	[-215:6877:1]	Generators of the group modulo torsion
j	31969289829351424000/6135368507583237	j-invariant
L	3.1916452296722	L(r)(E,1)/r!
Ω	0.31990324198345	Real period
R	0.66512720323047	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	14352bh1 57408x1 10764k1 89700r1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3588d1

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

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Quadratic twists for elliptic curve 3588d1

-4	8	-3	5	13	-23
14352bh1	57408x1	10764k1	89700r1	46644b1	82524d1

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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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