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	8	Product of Tamagawa factors cp
deg	10560	Modular degree for the optimal curve
Δ	-13451837571072 = -1 · 234 · 33 · 29	Discriminant
Eigenvalues	2- 3+  2 -4  0  2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-32739,-2286878]	[a1,a2,a3,a4,a6]
Generators	[1778381:17693610:6859]	Generators of the group modulo torsion
j	-35091039199419/121634816	j-invariant
L	3.7411879492999	L(r)(E,1)/r!
Ω	0.17742429216986	Real period
R	10.543054458738	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	522b1 16704bq1 4176o1 104400dj1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4176t1

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 4176t1

-4	8	-3	5	29
522b1	16704bq1	4176o1	104400dj1	121104bf1

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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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