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	50400dd	Isogeny class
Conductor	50400	Conductor
∏ cp	64	Product of Tamagawa factors cp
deg	1474560	Modular degree for the optimal curve
Δ	3.2957645765625E+19	Discriminant
Eigenvalues	2- 3- 5+ 7+  4  2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-4559925,3737679500]	[a1,a2,a3,a4,a6]
Generators	[109595:2542428:125]	Generators of the group modulo torsion
j	14383655824793536/45209390625	j-invariant
L	6.4501519225279	L(r)(E,1)/r!
Ω	0.20833816899802	Real period
R	7.7400026523898	Regulator
r	1	Rank of the group of rational points
S	0.99999999999584	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	50400bq1 100800ed2 16800e1 10080bb1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 50400dd1

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

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Quadratic twists for elliptic curve 50400dd1

-4	8	-3	5
50400bq1	100800ed2	16800e1	10080bb1

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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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