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	6384m	Isogeny class
Conductor	6384	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	-2758634928 = -1 · 24 · 33 · 72 · 194	Discriminant
Eigenvalues	2+ 3- -2 7-  0 -2  2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,321,1332]	[a1,a2,a3,a4,a6]
Generators	[12:84:1]	Generators of the group modulo torsion
j	227910944768/172414683	j-invariant
L	4.3910611117313	L(r)(E,1)/r!
Ω	0.91815865169304	Real period
R	1.5941548168661	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	3192b1 25536ck1 19152t1 44688l1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 6384m1

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	-	0	-2	2	+	4	2	0	-10	-10	-4	-12	-6	4	14	4	16	10	-16	-8	6	18

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Quadratic twists for elliptic curve 6384m1

-4	8	-3	-7	-19
3192b1	25536ck1	19152t1	44688l1	121296u1

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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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