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	50400dh	Isogeny class
Conductor	50400	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	-5040947520000000 = -1 · 212 · 38 · 57 · 74	Discriminant
Eigenvalues	2- 3- 5+ 7+ -4  2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,39300,1636000]	[a1,a2,a3,a4,a6]
Generators	[110:-2700:1]	Generators of the group modulo torsion
j	143877824/108045	j-invariant
L	5.1598902348513	L(r)(E,1)/r!
Ω	0.27585754104205	Real period
R	1.1690568199035	Regulator
r	1	Rank of the group of rational points
S	1.0000000000037	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	50400bm2 100800dz1 16800p4 10080u4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 50400dh2

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

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Quadratic twists for elliptic curve 50400dh2

-4	8	-3	5
50400bm2	100800dz1	16800p4	10080u4

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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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