Cremona's table of elliptic curves

6888 = 2³ · 3 · 7 · 41

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 41-	Signs for the Atkin-Lehner involutions
Class	6888a	Isogeny class
Conductor	6888	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	1518225408 = 211 · 32 · 72 · 412	Discriminant
Eigenvalues	2- 3-  0 7+  2  2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-288,-288]	[a1,a2,a3,a4,a6]
j	1294429250/741321	j-invariant
L	2.5127607877857	L(r)(E,1)/r!
Ω	1.2563803938929	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	13776c2 55104c2 20664e2 48216k2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 6888a2

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	-2	0	0	4	-4	-2	-	8	0	12	10	8	2	-8	2	8	14	-14	2

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Quadratic twists for elliptic curve 6888a2

-4	8	-3	-7
13776c2	55104c2	20664e2	48216k2

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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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