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	4176t	Isogeny class
Conductor	4176	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	190480121856 = 223 · 33 · 292	Discriminant
Eigenvalues	2- 3+  2 -4  0  2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-524259,-146105630]	[a1,a2,a3,a4,a6]
Generators	[8657:802560:1]	Generators of the group modulo torsion
j	144091275020705979/1722368	j-invariant
L	3.7411879492999	L(r)(E,1)/r!
Ω	0.17742429216986	Real period
R	5.2715272293692	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	522b2 16704bq2 4176o2 104400dj2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4176t2

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	-4	0	2	-2	0	4	-	-6	-4	-2	-4	-8	14	6	-8	12	-16	-2	6	-2	-14	-14

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Quadratic twists for elliptic curve 4176t2

-4	8	-3	5	29
522b2	16704bq2	4176o2	104400dj2	121104bf2

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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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