Cremona's table of elliptic curves

48800 = 2⁵ · 5² · 61

Field	Data	Notes
Atkin-Lehner	2- 5+ 61-	Signs for the Atkin-Lehner involutions
Class	48800n	Isogeny class
Conductor	48800	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-61000000000000 = -1 · 212 · 512 · 61	Discriminant
Eigenvalues	2- -2 5+  4 -4 -2  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,3967,-361937]	[a1,a2,a3,a4,a6]
Generators	[1497:57988:1]	Generators of the group modulo torsion
j	107850176/953125	j-invariant
L	4.1026250924055	L(r)(E,1)/r!
Ω	0.30861700340335	Real period
R	6.6467904346345	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	48800m2 97600bx1 9760c2	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 48800n2

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

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Quadratic twists for elliptic curve 48800n2

-4	8	5
48800m2	97600bx1	9760c2

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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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