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	8	Product of Tamagawa factors cp
deg	5760	Modular degree for the optimal curve
Δ	511805554128 = 24 · 310 · 114 · 37	Discriminant
Eigenvalues	2- 3+  0  0 11-  2 -4  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-9813,375858]	[a1,a2,a3,a4,a6]
Generators	[62:44:1]	Generators of the group modulo torsion
j	6532108386304000/31987847133	j-invariant
L	3.2875183731408	L(r)(E,1)/r!
Ω	0.93342518850267	Real period
R	1.7609972462894	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	19536z1 78144be1 14652c1 122100x1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4884c1

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 4884c1

-4	8	-3	5	-11
19536z1	78144be1	14652c1	122100x1	53724b1

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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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