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	50400cv	Isogeny class
Conductor	50400	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	7144200000000 = 29 · 36 · 58 · 72	Discriminant
Eigenvalues	2- 3- 5+ 7+  0  2  2  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-2940075,1940375250]	[a1,a2,a3,a4,a6]
Generators	[13970:369325:8]	Generators of the group modulo torsion
j	481927184300808/1225	j-invariant
L	6.5783971148581	L(r)(E,1)/r!
Ω	0.48990371489931	Real period
R	6.7139694135688	Regulator
r	1	Rank of the group of rational points
S	1.0000000000004	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	50400dl4 100800la4 5600a2 10080p3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 50400cv4

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	8	8	-6	0	2	6	-8	-8	-2	-8	-2	-8	0	-10	-16	16	-10	14

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Quadratic twists for elliptic curve 50400cv4

-4	8	-3	5
50400dl4	100800la4	5600a2	10080p3

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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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