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	82800bq	Isogeny class
Conductor	82800	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	19584392544000000 = 211 · 37 · 56 · 234	Discriminant
Eigenvalues	2+ 3- 5+ -4  0  2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-68475,-1493750]	[a1,a2,a3,a4,a6]
Generators	[-135:2300:1]	Generators of the group modulo torsion
j	1522096994/839523	j-invariant
L	5.4577632562505	L(r)(E,1)/r!
Ω	0.3158432129509	Real period
R	0.53999926164843	Regulator
r	1	Rank of the group of rational points
S	0.99999999981048	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	41400bu3 27600y3 3312b3	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 82800bq3

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	0	2	-2	4	-	2	8	-2	-10	-4	0	6	12	2	-12	-16	-10	4	0	-6	14

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Quadratic twists for elliptic curve 82800bq3

-4	-3	5
41400bu3	27600y3	3312b3

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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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