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	6384r	Isogeny class
Conductor	6384	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	3840	Modular degree for the optimal curve
Δ	-3369966768 = -1 · 24 · 35 · 74 · 192	Discriminant
Eigenvalues	2- 3+ -2 7+  2 -6  2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-229,-3020]	[a1,a2,a3,a4,a6]
j	-83369132032/210622923	j-invariant
L	0.57111913113389	L(r)(E,1)/r!
Ω	0.57111913113389	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1596e1 25536cy1 19152bm1 44688dl1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 6384r1

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

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Quadratic twists for elliptic curve 6384r1

-4	8	-3	-7	-19
1596e1	25536cy1	19152bm1	44688dl1	121296cr1

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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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