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	6864j	Isogeny class
Conductor	6864	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	846720	Modular degree for the optimal curve
Δ	-1.0736094776402E+23	Discriminant
Eigenvalues	2- 3+ -1 -1 11+ 13+  4 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-92390416,-342145483328]	[a1,a2,a3,a4,a6]
j	-21293376668673906679951249/26211168887701209984	j-invariant
L	0.77907766772266	L(r)(E,1)/r!
Ω	0.024346177116333	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	858k1 27456cj1 20592bl1 75504bt1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 6864j1

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
-	+	-1	-1	+	+	4	-6	-3	-5	-4	10	-7	5	8	-2	3	13	9	-2	-3	-10	14	-8	-14

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Quadratic twists for elliptic curve 6864j1

-4	8	-3	-11	13
858k1	27456cj1	20592bl1	75504bt1	89232bh1

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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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