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	50400dk	Isogeny class
Conductor	50400	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-247006428480000000 = -1 · 212 · 38 · 57 · 76	Discriminant
Eigenvalues	2- 3- 5+ 7+ -6 -4  6  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-302700,68416000]	[a1,a2,a3,a4,a6]
Generators	[260:2700:1]	Generators of the group modulo torsion
j	-65743598656/5294205	j-invariant
L	4.8379109343863	L(r)(E,1)/r!
Ω	0.30581408192403	Real period
R	1.9774722700633	Regulator
r	1	Rank of the group of rational points
S	0.9999999999978	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	50400dy2 100800mq1 16800t2 10080v2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 50400dk2

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
-	-	+	+	-6	-4	6	6	-4	2	-2	-6	-6	12	0	-4	4	-10	12	-2	-16	4	-12	6	12

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Quadratic twists for elliptic curve 50400dk2

-4	8	-3	5
50400dy2	100800mq1	16800t2	10080v2

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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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