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	50400dz	Isogeny class
Conductor	50400	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	-7085592211235328000 = -1 · 212 · 324 · 53 · 72	Discriminant
Eigenvalues	2- 3- 5- 7+  2  2  0 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-8266620,-9149189600]	[a1,a2,a3,a4,a6]
j	-167382537005851712/18983603961	j-invariant
L	2.8491452110416	L(r)(E,1)/r!
Ω	0.044517893922329	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	50400by2 100800gu1 16800y2 50400bv2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 50400dz2

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
-	-	-	+	2	2	0	-6	8	-6	10	8	6	4	8	2	12	14	8	-2	2	-8	0	-6	14

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Quadratic twists for elliptic curve 50400dz2

-4	8	-3	5
50400by2	100800gu1	16800y2	50400bv2

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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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