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	4176bb	Isogeny class
Conductor	4176	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	-4676050944 = -1 · 213 · 39 · 29	Discriminant
Eigenvalues	2- 3- -1 -1  6 -4  7  3	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-723,-8174]	[a1,a2,a3,a4,a6]
j	-13997521/1566	j-invariant
L	1.8298548342178	L(r)(E,1)/r!
Ω	0.45746370855446	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	522e1 16704ce1 1392m1 104400ei1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4176bb1

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
-	-	-1	-1	6	-4	7	3	4	-	0	-7	-5	5	-5	-10	3	10	0	-4	10	6	16	10	-8

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Quadratic twists for elliptic curve 4176bb1

-4	8	-3	5	29
522e1	16704ce1	1392m1	104400ei1	121104bu1

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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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