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
Δ	578942926848 = 220 · 33 · 112 · 132	Discriminant
Eigenvalues	2- 3-  4  0 11+ 13-  0  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-589776,174136212]	[a1,a2,a3,a4,a6]
j	5538928862777598289/141343488	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	858i2 27456bt2 20592by2 75504cs2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 6864x2

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 6864x2

-4	8	-3	-11	13
858i2	27456bt2	20592by2	75504cs2	89232ct2

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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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