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	1176f	Isogeny class
Conductor	1176	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	144	Modular degree for the optimal curve
Δ	-338688 = -1 · 28 · 33 · 72	Discriminant
Eigenvalues	2+ 3- -2 7- -6  3 -4  5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-9,27]	[a1,a2,a3,a4,a6]
Generators	[3:-6:1]	Generators of the group modulo torsion
j	-7168/27	j-invariant
L	2.6944116628682	L(r)(E,1)/r!
Ω	2.6560563607573	Real period
R	0.084536724655569	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	2352e1 9408l1 3528z1 29400cz1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1176f1

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	-	-6	3	-4	5	-4	-4	-7	-9	2	-1	-2	8	0	-10	-15	-6	11	1	-6	8	14

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Quadratic twists for elliptic curve 1176f1

-4	8	-3	5	-7
2352e1	9408l1	3528z1	29400cz1	1176a1

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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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