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	6384bb	Isogeny class
Conductor	6384	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	7545581568 = 212 · 36 · 7 · 192	Discriminant
Eigenvalues	2- 3-  0 7+  2  0 -4 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-768,-7308]	[a1,a2,a3,a4,a6]
Generators	[-12:18:1]	Generators of the group modulo torsion
j	12246522625/1842183	j-invariant
L	4.7661489190948	L(r)(E,1)/r!
Ω	0.91594564557399	Real period
R	0.86725468593135	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	399b2 25536bu2 19152bk2 44688ch2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 6384bb2

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

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Quadratic twists for elliptic curve 6384bb2

-4	8	-3	-7	-19
399b2	25536bu2	19152bk2	44688ch2	121296bw2

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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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