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	8400f	Isogeny class
Conductor	8400	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	3024000000 = 210 · 33 · 56 · 7	Discriminant
Eigenvalues	2+ 3+ 5+ 7-  0 -6  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-100808,-12285888]	[a1,a2,a3,a4,a6]
j	7080974546692/189	j-invariant
L	1.0717301242352	L(r)(E,1)/r!
Ω	0.26793253105879	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	4200x4 33600gl4 25200bn4 336c3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8400f3

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

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Quadratic twists for elliptic curve 8400f3

-4	8	-3	5	-7
4200x4	33600gl4	25200bn4	336c3	58800cw4

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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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