Cremona's table of elliptic curves

8400 = 2⁴ · 3 · 5² · 7

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 7-	Signs for the Atkin-Lehner involutions
Class	8400cg	Isogeny class
Conductor	8400	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	840000000000 = 212 · 3 · 510 · 7	Discriminant
Eigenvalues	2- 3- 5+ 7-  0  6 -2  8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-45008,3659988]	[a1,a2,a3,a4,a6]
j	157551496201/13125	j-invariant
L	3.4014523727476	L(r)(E,1)/r!
Ω	0.85036309318691	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	525a3 33600ez4 25200ei4 1680n3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8400cg3

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
-	-	+	-	0	6	-2	8	8	-2	-4	2	-6	4	8	-10	-4	-2	4	12	2	-8	-4	-6	18

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Quadratic twists for elliptic curve 8400cg3

-4	8	-3	5	-7
525a3	33600ez4	25200ei4	1680n3	58800fj4

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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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