Cremona's table of elliptic curves

1147 = 31 · 37

Field	Data	Notes
Atkin-Lehner	31- 37+	Signs for the Atkin-Lehner involutions
Class	1147a	Isogeny class
Conductor	1147	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	80	Modular degree for the optimal curve
Δ	35557 = 312 · 37	Discriminant
Eigenvalues	0 -1 -2 -5 -3 -2  0 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-9,9]	[a1,a2,a3,a4,a6]
Generators	[1:0:1] [7:15:1]	Generators of the group modulo torsion
j	89915392/35557	j-invariant
L	1.9446042796924	L(r)(E,1)/r!
Ω	3.3341015496648	Real period
R	0.29162343298846	Regulator
r	2	Rank of the group of rational points
S	1.0000000000008	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	18352f1 73408q1 10323c1 28675d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1147a1

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	-1	-2	-5	-3	-2	0	-6	0	-4	-	+	-5	6	-9	-5	-6	8	-4	1	-11	-10	-17	8	-6

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Quadratic twists for elliptic curve 1147a1

-4	8	-3	5	-7	-31	37
18352f1	73408q1	10323c1	28675d1	56203a1	35557c1	42439a1

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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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