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	50400s	Isogeny class
Conductor	50400	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	4538743123320000000 = 29 · 39 · 57 · 78	Discriminant
Eigenvalues	2+ 3- 5+ 7+  0 -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-504075,92025250]	[a1,a2,a3,a4,a6]
j	2428799546888/778248135	j-invariant
L	0.90465442166273	L(r)(E,1)/r!
Ω	0.22616360545908	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	50400dn3 100800cw3 16800br2 10080bp3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 50400s3

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

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Quadratic twists for elliptic curve 50400s3

-4	8	-3	5
50400dn3	100800cw3	16800br2	10080bp3

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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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