Cremona's table of elliptic curves

4176 = 2⁴ · 3² · 29

Field	Data	Notes
Atkin-Lehner	2- 3- 29+	Signs for the Atkin-Lehner involutions
Class	4176z	Isogeny class
Conductor	4176	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	-1014768 = -1 · 24 · 37 · 29	Discriminant
Eigenvalues	2- 3- -2 -1  1 -3  3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-21,-61]	[a1,a2,a3,a4,a6]
Generators	[10:27:1]	Generators of the group modulo torsion
j	-87808/87	j-invariant
L	3.1375288112819	L(r)(E,1)/r!
Ω	1.0721364584704	Real period
R	1.4632133747966	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	1044f1 16704dd1 1392l1 104400dq1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4176z1

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	-1	1	-3	3	-2	8	+	8	0	-2	0	5	2	-6	-12	-3	4	-16	2	-6	-3	-6

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Quadratic twists for elliptic curve 4176z1

-4	8	-3	5	29
1044f1	16704dd1	1392l1	104400dq1	121104cb1

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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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