Cremona's table of elliptic curves

6800 = 2⁴ · 5² · 17

Field	Data	Notes
Atkin-Lehner	2- 5+ 17+	Signs for the Atkin-Lehner involutions
Class	6800l	Isogeny class
Conductor	6800	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	27200000000 = 212 · 58 · 17	Discriminant
Eigenvalues	2-  2 5+ -2 -2 -2 17+  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3408,77312]	[a1,a2,a3,a4,a6]
j	68417929/425	j-invariant
L	2.3844793164442	L(r)(E,1)/r!
Ω	1.1922396582221	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	425d1 27200ce1 61200fs1 1360g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6800l1

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	+	-2	-2	-2	+	0	6	-6	10	-2	10	4	12	10	-8	-14	8	2	14	14	4	6	-2

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Quadratic twists for elliptic curve 6800l1

-4	8	-3	5	17
425d1	27200ce1	61200fs1	1360g1	115600ca1

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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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