Cremona's table of elliptic curves

5538 = 2 · 3 · 13 · 71

Field	Data	Notes
Atkin-Lehner	2+ 3+ 13- 71-	Signs for the Atkin-Lehner involutions
Class	5538f	Isogeny class
Conductor	5538	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	21742276608 = 212 · 34 · 13 · 712	Discriminant
Eigenvalues	2+ 3+  2 -4 -4 13- -6  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-1431590229,-20849163135507]	[a1,a2,a3,a4,a6]
Generators	[430931705148890672873995182861:-351575102493125480625752408067378:646088474394578011469401]	Generators of the group modulo torsion
j	324473989984535866803447669981913/21742276608	j-invariant
L	2.295497098662	L(r)(E,1)/r!
Ω	0.024543973493674	Real period
R	46.762947720214	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	44304p4 16614t4 71994bc4	Quadratic twists by: -4 -3 13

Hecke Eigenvalues for elliptic curve 5538f3

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

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Quadratic twists for elliptic curve 5538f3

-4	-3	13
44304p4	16614t4	71994bc4

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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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