Cremona's table of elliptic curves

82800 = 2⁴ · 3² · 5² · 23

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 23+	Signs for the Atkin-Lehner involutions
Class	82800z	Isogeny class
Conductor	82800	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	347076900000000 = 28 · 38 · 58 · 232	Discriminant
Eigenvalues	2+ 3- 5+  4  4 -6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-35175,2375750]	[a1,a2,a3,a4,a6]
j	1650587344/119025	j-invariant
L	2.1137176626651	L(r)(E,1)/r!
Ω	0.52842943070946	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	41400o2 27600j2 16560v2	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 82800z2

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

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Quadratic twists for elliptic curve 82800z2

-4	-3	5
41400o2	27600j2	16560v2

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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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