Cremona's table of elliptic curves

6864 = 2⁴ · 3 · 11 · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 11+ 13-	Signs for the Atkin-Lehner involutions
Class	6864m	Isogeny class
Conductor	6864	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	5376	Modular degree for the optimal curve
Δ	-142264629936 = -1 · 24 · 314 · 11 · 132	Discriminant
Eigenvalues	2- 3+ -2  2 11+ 13-  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-109,-18116]	[a1,a2,a3,a4,a6]
Generators	[18568:79833:512]	Generators of the group modulo torsion
j	-9033613312/8891539371	j-invariant
L	3.205192858329	L(r)(E,1)/r!
Ω	0.46607510197059	Real period
R	6.8769879463144	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	1716c1 27456ce1 20592bu1 75504bl1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 6864m1

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

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Quadratic twists for elliptic curve 6864m1

-4	8	-3	-11	13
1716c1	27456ce1	20592bu1	75504bl1	89232bl1

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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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