Cremona's table of elliptic curves

1176 = 2³ · 3 · 7²

Field	Data	Notes
Atkin-Lehner	2- 3+ 7-	Signs for the Atkin-Lehner involutions
Class	1176g	Isogeny class
Conductor	1176	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	128	Modular degree for the optimal curve
Δ	-790272 = -1 · 28 · 32 · 73	Discriminant
Eigenvalues	2- 3+  0 7-  0 -4 -4  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,12,36]	[a1,a2,a3,a4,a6]
Generators	[0:6:1]	Generators of the group modulo torsion
j	2000/9	j-invariant
L	2.2517830789797	L(r)(E,1)/r!
Ω	2.0287142597755	Real period
R	0.27748894011679	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	2352g1 9408y1 3528i1 29400bl1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1176g1

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

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Quadratic twists for elliptic curve 1176g1

-4	8	-3	5	-7
2352g1	9408y1	3528i1	29400bl1	1176h1

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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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