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	6384v	Isogeny class
Conductor	6384	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	33792	Modular degree for the optimal curve
Δ	-5898550563066672 = -1 · 24 · 311 · 78 · 192	Discriminant
Eigenvalues	2- 3+  2 7- -6  2 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,43843,1066632]	[a1,a2,a3,a4,a6]
Generators	[1348:50078:1]	Generators of the group modulo torsion
j	582498235727347712/368659410191667	j-invariant
L	3.8484285105344	L(r)(E,1)/r!
Ω	0.26468710799619	Real period
R	3.6348847320794	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	1596c1 25536dq1 19152bv1 44688dr1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 6384v1

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

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Quadratic twists for elliptic curve 6384v1

-4	8	-3	-7	-19
1596c1	25536dq1	19152bv1	44688dr1	121296dh1

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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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