Cremona's table of elliptic curves

176 = 2⁴ · 11

Field	Data	Notes
Atkin-Lehner	2- 11-	Signs for the Atkin-Lehner involutions
Class	176c	Isogeny class
Conductor	176	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	8	Modular degree for the optimal curve
Δ	-2816 = -1 · 28 · 11	Discriminant
Eigenvalues	2- -1 -3 -2 11- -4  6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,3,1]	[a1,a2,a3,a4,a6]
Generators	[1:2:1]	Generators of the group modulo torsion
j	8192/11	j-invariant
L	1.0693142864076	L(r)(E,1)/r!
Ω	3.0540697209359	Real period
R	0.17506383025203	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	44a1 704f1 1584o1 4400s1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 176c1

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	-3	-2	-	-4	6	-8	3	0	-5	-1	0	10	0	-6	-3	-4	1	-15	-4	-2	-6	-9	-7

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Quadratic twists for elliptic curve 176c1

-4	8	-3	5	-7	-11	13	17	-19	-23
44a1	704f1	1584o1	4400s1	8624ba1	1936h1	29744o1	50864bd1	63536bm1	93104n1

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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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