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	6864p	Isogeny class
Conductor	6864	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	268625337552 = 24 · 36 · 116 · 13	Discriminant
Eigenvalues	2- 3+  0 -2 11- 13-  6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-7676773,8189396800]	[a1,a2,a3,a4,a6]
j	3127086412733145284608000/16789083597	j-invariant
L	1.4229490798248	L(r)(E,1)/r!
Ω	0.4743163599416	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1716b3 27456bx3 20592be3 75504bg3	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 6864p3

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

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Quadratic twists for elliptic curve 6864p3

-4	8	-3	-11	13
1716b3	27456bx3	20592be3	75504bg3	89232x3

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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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