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	50400dj	Isogeny class
Conductor	50400	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	210039480000000 = 29 · 37 · 57 · 74	Discriminant
Eigenvalues	2- 3- 5+ 7+ -4 -6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-39675,2960750]	[a1,a2,a3,a4,a6]
Generators	[-115:2450:1]	Generators of the group modulo torsion
j	1184287112/36015	j-invariant
L	4.2571461937742	L(r)(E,1)/r!
Ω	0.55975394981044	Real period
R	0.95067354932985	Regulator
r	1	Rank of the group of rational points
S	1.0000000000077	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	50400bp3 100800eb3 16800d2 10080bc3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 50400dj3

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

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Quadratic twists for elliptic curve 50400dj3

-4	8	-3	5
50400bp3	100800eb3	16800d2	10080bc3

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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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