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	82800cm	Isogeny class
Conductor	82800	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	995328	Modular degree for the optimal curve
Δ	1302331392000000000 = 230 · 33 · 59 · 23	Discriminant
Eigenvalues	2- 3+ 5+ -4  0  4  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-276675,-11090750]	[a1,a2,a3,a4,a6]
j	1355469437763/753664000	j-invariant
L	1.7858592934488	L(r)(E,1)/r!
Ω	0.22323240482567	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	10350e1 82800ct3 16560bg1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 82800cm1

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

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Quadratic twists for elliptic curve 82800cm1

-4	-3	5
10350e1	82800ct3	16560bg1

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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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