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	6800d	Isogeny class
Conductor	6800	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-4624000000 = -1 · 210 · 56 · 172	Discriminant
Eigenvalues	2+ -2 5+ -2  6 -2 17+  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,392,-1212]	[a1,a2,a3,a4,a6]
Generators	[8:50:1]	Generators of the group modulo torsion
j	415292/289	j-invariant
L	2.705477711021	L(r)(E,1)/r!
Ω	0.77660059930171	Real period
R	0.87093601056117	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3400c2 27200cb2 61200bw2 272c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6800d2

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

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Quadratic twists for elliptic curve 6800d2

-4	8	-3	5	17
3400c2	27200cb2	61200bw2	272c2	115600g2

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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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