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	6864x	Isogeny class
Conductor	6864	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	27648	Modular degree for the optimal curve
Δ	-27983590981632 = -1 · 228 · 36 · 11 · 13	Discriminant
Eigenvalues	2- 3-  4  0 11+ 13-  0  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-36816,2718612]	[a1,a2,a3,a4,a6]
j	-1347365318848849/6831931392	j-invariant
L	4.0127297495931	L(r)(E,1)/r!
Ω	0.66878829159885	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	858i1 27456bt1 20592by1 75504cs1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 6864x1

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

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Quadratic twists for elliptic curve 6864x1

-4	8	-3	-11	13
858i1	27456bt1	20592by1	75504cs1	89232ct1

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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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