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	6384f	Isogeny class
Conductor	6384	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	1551312 = 24 · 36 · 7 · 19	Discriminant
Eigenvalues	2+ 3+ -4 7- -4  2 -4 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-35,66]	[a1,a2,a3,a4,a6]
Generators	[6:6:1]	Generators of the group modulo torsion
j	304900096/96957	j-invariant
L	2.3964531402293	L(r)(E,1)/r!
Ω	2.4745440296668	Real period
R	1.9368846231861	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	3192o1 25536di1 19152bb1 44688bf1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 6384f1

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	-	-4	2	-4	-	0	4	8	-2	-6	-12	10	0	12	-2	8	-6	14	8	-6	2	2

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Quadratic twists for elliptic curve 6384f1

-4	8	-3	-7	-19
3192o1	25536di1	19152bb1	44688bf1	121296bp1

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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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