Cremona's table of elliptic curves

4148 = 2² · 17 · 61

Field	Data	Notes
Atkin-Lehner	2- 17+ 61-	Signs for the Atkin-Lehner involutions
Class	4148a	Isogeny class
Conductor	4148	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	9984	Modular degree for the optimal curve
Δ	-108933428198656 = -1 · 28 · 178 · 61	Discriminant
Eigenvalues	2-  0 -3  1  3  1 17+ -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,241,-502154]	[a1,a2,a3,a4,a6]
Generators	[16395:167042:125]	Generators of the group modulo torsion
j	6046929072/425521203901	j-invariant
L	3.0489583962834	L(r)(E,1)/r!
Ω	0.27347658975745	Real period
R	1.858147101968	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	16592b1 66368b1 37332c1 103700g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4148a1

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	-3	1	3	1	+	-6	7	0	8	6	5	0	-12	6	-11	-	-7	-4	-11	-13	-4	0	-2

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Quadratic twists for elliptic curve 4148a1

-4	8	-3	5	17
16592b1	66368b1	37332c1	103700g1	70516b1

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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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