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	6864k	Isogeny class
Conductor	6864	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	24192	Modular degree for the optimal curve
Δ	-53520057237504 = -1 · 226 · 3 · 112 · 133	Discriminant
Eigenvalues	2- 3+  2 -4 11+ 13+ -8  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-5312,384000]	[a1,a2,a3,a4,a6]
j	-4047806261953/13066420224	j-invariant
L	1.1064649074302	L(r)(E,1)/r!
Ω	0.55323245371512	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	858l1 27456co1 20592bo1 75504bv1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 6864k1

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	-4	+	+	-8	6	6	-2	2	4	2	-4	-4	-8	-12	-2	-12	16	0	8	-4	10	10

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Quadratic twists for elliptic curve 6864k1

-4	8	-3	-11	13
858l1	27456co1	20592bo1	75504bv1	89232bo1

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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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