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	6864u	Isogeny class
Conductor	6864	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	56131485696 = 215 · 32 · 114 · 13	Discriminant
Eigenvalues	2- 3-  2  0 11+ 13+  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-79912,8668340]	[a1,a2,a3,a4,a6]
Generators	[188:570:1]	Generators of the group modulo torsion
j	13778603383488553/13703976	j-invariant
L	5.4472022725019	L(r)(E,1)/r!
Ω	0.9367813622215	Real period
R	2.9074032064346	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	858a3 27456bw4 20592bn3 75504cx4	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 6864u4

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

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Quadratic twists for elliptic curve 6864u4

-4	8	-3	-11	13
858a3	27456bw4	20592bn3	75504cx4	89232cq4

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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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