Cremona's table of elliptic curves

50400 = 2⁵ · 3² · 5² · 7

Field	Data	Notes
Atkin-Lehner	2+ 3- 5- 7-	Signs for the Atkin-Lehner involutions
Class	50400by	Isogeny class
Conductor	50400	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-7085592211235328000 = -1 · 212 · 324 · 53 · 72	Discriminant
Eigenvalues	2+ 3- 5- 7- -2  2  0  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-8266620,9149189600]	[a1,a2,a3,a4,a6]
j	-167382537005851712/18983603961	j-invariant
L	1.8129493984416	L(r)(E,1)/r!
Ω	0.22661867493164	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	50400dz2 100800hq1 16800bk2 50400ea2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 50400by2

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

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Quadratic twists for elliptic curve 50400by2

-4	8	-3	5
50400dz2	100800hq1	16800bk2	50400ea2

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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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