Cremona's table of elliptic curves

4884 = 2² · 3 · 11 · 37

Field	Data	Notes
Atkin-Lehner	2- 3+ 11- 37+	Signs for the Atkin-Lehner involutions
Class	4884c	Isogeny class
Conductor	4884	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	10304692992 = 28 · 35 · 112 · 372	Discriminant
Eigenvalues	2- 3+  0  0 11-  2 -4  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-156828,23957064]	[a1,a2,a3,a4,a6]
Generators	[821:21164:1]	Generators of the group modulo torsion
j	1666315860501346000/40252707	j-invariant
L	3.2875183731408	L(r)(E,1)/r!
Ω	0.93342518850267	Real period
R	3.5219944925789	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	19536z2 78144be2 14652c2 122100x2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4884c2

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

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Quadratic twists for elliptic curve 4884c2

-4	8	-3	5	-11
19536z2	78144be2	14652c2	122100x2	53724b2

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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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