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	6384x	Isogeny class
Conductor	6384	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	3840	Modular degree for the optimal curve
Δ	3706601472 = 214 · 35 · 72 · 19	Discriminant
Eigenvalues	2- 3+ -2 7-  2  2 -4 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1464,-20880]	[a1,a2,a3,a4,a6]
Generators	[-22:14:1]	Generators of the group modulo torsion
j	84778086457/904932	j-invariant
L	3.1321887420346	L(r)(E,1)/r!
Ω	0.77227079078644	Real period
R	2.0279083317685	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	798c1 25536dn1 19152bt1 44688dk1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 6384x1

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

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Quadratic twists for elliptic curve 6384x1

-4	8	-3	-7	-19
798c1	25536dn1	19152bt1	44688dk1	121296dj1

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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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