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	50400eh	Isogeny class
Conductor	50400	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	28800	Modular degree for the optimal curve
Δ	-11430720000 = -1 · 29 · 36 · 54 · 72	Discriminant
Eigenvalues	2- 3- 5- 7-  3  2  5 -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-75,5150]	[a1,a2,a3,a4,a6]
Generators	[5:-70:1]	Generators of the group modulo torsion
j	-200/49	j-invariant
L	7.1530118871825	L(r)(E,1)/r!
Ω	1.0385442855062	Real period
R	0.57396139216168	Regulator
r	1	Rank of the group of rational points
S	1.000000000002	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	50400bu1 100800ie1 5600j1 50400y1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 50400eh1

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
-	-	-	-	3	2	5	-1	-4	-10	8	0	9	-8	-6	0	-12	-6	-1	14	-11	6	7	-9	-18

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Quadratic twists for elliptic curve 50400eh1

-4	8	-3	5
50400bu1	100800ie1	5600j1	50400y1

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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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