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	6384w	Isogeny class
Conductor	6384	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	-41604528 = -1 · 24 · 3 · 74 · 192	Discriminant
Eigenvalues	2- 3+ -2 7-  2  2  2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-309,2220]	[a1,a2,a3,a4,a6]
Generators	[8:14:1]	Generators of the group modulo torsion
j	-204589760512/2600283	j-invariant
L	3.1767498699167	L(r)(E,1)/r!
Ω	2.0426344444757	Real period
R	0.77761096179204	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	1596d1 25536dm1 19152bs1 44688dj1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 6384w1

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

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Quadratic twists for elliptic curve 6384w1

-4	8	-3	-7	-19
1596d1	25536dm1	19152bs1	44688dj1	121296di1

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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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