Cremona's table of elliptic curves

6384 = 2⁴ · 3 · 7 · 19

Field	Data	Notes
Atkin-Lehner	2+ 3- 7- 19+	Signs for the Atkin-Lehner involutions
Class	6384m	Isogeny class
Conductor	6384	Conductor
∏ cp	96	Product of Tamagawa factors cp
Δ	3028319142912 = 210 · 33 · 78 · 19	Discriminant
Eigenvalues	2+ 3- -2 7-  0 -2  2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-11744,-486588]	[a1,a2,a3,a4,a6]
Generators	[-62:84:1]	Generators of the group modulo torsion
j	174947951977348/2957342913	j-invariant
L	4.3910611117313	L(r)(E,1)/r!
Ω	0.45907932584652	Real period
R	0.39853870421653	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	3192b4 25536ck3 19152t4 44688l3	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 6384m3

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	-	0	-2	2	+	4	2	0	-10	-10	-4	-12	-6	4	14	4	16	10	-16	-8	6	18

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Quadratic twists for elliptic curve 6384m3

-4	8	-3	-7	-19
3192b4	25536ck3	19152t4	44688l3	121296u3

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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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