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	4176y	Isogeny class
Conductor	4176	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-309047127963918336 = -1 · 213 · 37 · 297	Discriminant
Eigenvalues	2- 3-  1 -1 -2  0  3  1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-937587,-350456398]	[a1,a2,a3,a4,a6]
Generators	[3031:157014:1]	Generators of the group modulo torsion
j	-30526075007211889/103499257854	j-invariant
L	3.7548374764312	L(r)(E,1)/r!
Ω	0.076697022577693	Real period
R	6.119594591543	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	522d2 16704db2 1392k2 104400dr2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4176y2

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	-2	0	3	1	-4	+	-4	3	7	-9	-1	2	-3	6	-12	16	-10	-10	0	-6	0

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Quadratic twists for elliptic curve 4176y2

-4	8	-3	5	29
522d2	16704db2	1392k2	104400dr2	121104bt2

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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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