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	24	Product of Tamagawa factors cp
Δ	356091914221984512 = 28 · 39 · 114 · 136	Discriminant
Eigenvalues	2- 3+  0 -2 11- 13-  6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-193588,-15763556]	[a1,a2,a3,a4,a6]
j	3134160907827154000/1390984039929627	j-invariant
L	1.4229490798248	L(r)(E,1)/r!
Ω	0.2371581799708	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	1716b2 27456bx2 20592be2 75504bg2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 6864p2

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 6864p2

-4	8	-3	-11	13
1716b2	27456bx2	20592be2	75504bg2	89232x2

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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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