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
Δ	-1222384214016 = -1 · 213 · 310 · 7 · 192	Discriminant
Eigenvalues	2- 3+ -2 7-  2  2 -4 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-344,-53136]	[a1,a2,a3,a4,a6]
Generators	[90:798:1]	Generators of the group modulo torsion
j	-1102302937/298433646	j-invariant
L	3.1321887420346	L(r)(E,1)/r!
Ω	0.38613539539322	Real period
R	4.055816663537	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	798c2 25536dn2 19152bt2 44688dk2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 6384x2

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 6384x2

-4	8	-3	-7	-19
798c2	25536dn2	19152bt2	44688dk2	121296dj2

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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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