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	6384a	Isogeny class
Conductor	6384	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	6435072 = 28 · 33 · 72 · 19	Discriminant
Eigenvalues	2+ 3+ -4 7+ -2 -4  4 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-180,-864]	[a1,a2,a3,a4,a6]
Generators	[-7:2:1]	Generators of the group modulo torsion
j	2533446736/25137	j-invariant
L	2.1439372837321	L(r)(E,1)/r!
Ω	1.303589149912	Real period
R	1.644641859651	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	3192p1 25536cz1 19152o1 44688bj1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 6384a1

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

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Quadratic twists for elliptic curve 6384a1

-4	8	-3	-7	-19
3192p1	25536cz1	19152o1	44688bj1	121296bc1

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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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