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	6800c	Isogeny class
Conductor	6800	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-1806250000000000 = -1 · 210 · 514 · 172	Discriminant
Eigenvalues	2+  2 5+  2  2 -2 17+ -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-88008,10284512]	[a1,a2,a3,a4,a6]
Generators	[62:2250:1]	Generators of the group modulo torsion
j	-4711672753924/112890625	j-invariant
L	5.9067875375245	L(r)(E,1)/r!
Ω	0.46945737845953	Real period
R	3.1455398341522	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	3400d2 27200cd2 61200bt2 1360c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6800c2

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

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Quadratic twists for elliptic curve 6800c2

-4	8	-3	5	17
3400d2	27200cd2	61200bt2	1360c2	115600k2

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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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