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	8400cf	Isogeny class
Conductor	8400	Conductor
∏ cp	192	Product of Tamagawa factors cp
Δ	571536000000000000 = 216 · 36 · 512 · 72	Discriminant
Eigenvalues	2- 3- 5+ 7-  0 -2  6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-231008,-22512012]	[a1,a2,a3,a4,a6]
j	21302308926361/8930250000	j-invariant
L	2.7125300609339	L(r)(E,1)/r!
Ω	0.22604417174449	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	1050k2 33600ey2 25200eg2 1680m2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8400cf2

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

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Quadratic twists for elliptic curve 8400cf2

-4	8	-3	5	-7
1050k2	33600ey2	25200eg2	1680m2	58800fe2

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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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