Cremona's table of elliptic curves

5382 = 2 · 3² · 13 · 23

Field	Data	Notes
Atkin-Lehner	2+ 3- 13- 23-	Signs for the Atkin-Lehner involutions
Class	5382g	Isogeny class
Conductor	5382	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	413720292492 = 22 · 37 · 132 · 234	Discriminant
Eigenvalues	2+ 3- -2 -4 -4 13- -6  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-97443,11732121]	[a1,a2,a3,a4,a6]
Generators	[-285:4179:1] [-216:4869:1]	Generators of the group modulo torsion
j	140362349594221873/567517548	j-invariant
L	3.2367991422573	L(r)(E,1)/r!
Ω	0.83114884435783	Real period
R	0.97359190361284	Regulator
r	2	Rank of the group of rational points
S	1.0000000000005	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	43056bo4 1794j3 69966bg4 123786u4	Quadratic twists by: -4 -3 13 -23

Hecke Eigenvalues for elliptic curve 5382g4

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

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Quadratic twists for elliptic curve 5382g4

-4	-3	13	-23
43056bo4	1794j3	69966bg4	123786u4

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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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