Cremona's table of elliptic curves

48400 = 2⁴ · 5² · 11²

Field	Data	Notes
Atkin-Lehner	2- 5+ 11-	Signs for the Atkin-Lehner involutions
Class	48400br	Isogeny class
Conductor	48400	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	8299975872320000000 = 212 · 57 · 1110	Discriminant
Eigenvalues	2-  0 5+  0 11-  2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1412675,-631226750]	[a1,a2,a3,a4,a6]
Generators	[-759:1936:1]	Generators of the group modulo torsion
j	2749884201/73205	j-invariant
L	5.8110757463798	L(r)(E,1)/r!
Ω	0.13870581511108	Real period
R	2.6184355274302	Regulator
r	1	Rank of the group of rational points
S	1.000000000002	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3025b4 9680w3 4400q4	Quadratic twists by: -4 5 -11

Hecke Eigenvalues for elliptic curve 48400br3

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
-	0	+	0	-	2	6	-4	4	-6	8	2	-2	-4	-12	2	-4	10	-16	-8	14	8	4	10	-10

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Quadratic twists for elliptic curve 48400br3

-4	5	-11
3025b4	9680w3	4400q4

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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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