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	50400bc	Isogeny class
Conductor	50400	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	1632960000000 = 212 · 36 · 57 · 7	Discriminant
Eigenvalues	2+ 3- 5+ 7+ -4 -2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-42300,-3348000]	[a1,a2,a3,a4,a6]
Generators	[280:2600:1] [456:8496:1]	Generators of the group modulo torsion
j	179406144/35	j-invariant
L	9.3329245136797	L(r)(E,1)/r!
Ω	0.33290440899521	Real period
R	14.01742401347	Regulator
r	2	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	50400du4 100800dx1 5600k3 10080cf2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 50400bc4

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

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Quadratic twists for elliptic curve 50400bc4

-4	8	-3	5
50400du4	100800dx1	5600k3	10080cf2

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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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