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	6864z	Isogeny class
Conductor	6864	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	18347472 = 24 · 36 · 112 · 13	Discriminant
Eigenvalues	2- 3-  0  2 11- 13- -2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-533,-4914]	[a1,a2,a3,a4,a6]
Generators	[34:132:1]	Generators of the group modulo torsion
j	1048576000000/1146717	j-invariant
L	5.2151609634001	L(r)(E,1)/r!
Ω	0.99352406036286	Real period
R	1.7497180563147	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	1716a1 27456bj1 20592bd1 75504ci1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 6864z1

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	-	-	-2	-6	-8	-2	6	-6	-8	8	-12	-10	8	2	-6	8	-2	-12	-8	0	-18

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Quadratic twists for elliptic curve 6864z1

-4	8	-3	-11	13
1716a1	27456bj1	20592bd1	75504ci1	89232bu1

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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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