Cremona's table of elliptic curves

1147 = 31 · 37

Field	Data	Notes
Atkin-Lehner	31- 37-	Signs for the Atkin-Lehner involutions
Class	1147b	Isogeny class
Conductor	1147	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	3920	Modular degree for the optimal curve
Δ	66639542677 = 312 · 375	Discriminant
Eigenvalues	-2 -1 -4  3 -3  4 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-26790,1696662]	[a1,a2,a3,a4,a6]
Generators	[117:387:1]	Generators of the group modulo torsion
j	2126464142970105856/66639542677	j-invariant
L	0.94208257709513	L(r)(E,1)/r!
Ω	1.0261943568604	Real period
R	2.2950880863771	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	5	Number of elements in the torsion subgroup
Twists	18352i1 73408k1 10323e1 28675c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1147b1

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	-1	-4	3	-3	4	-2	0	4	0	-	-	7	4	3	-1	-10	-8	-12	-3	-11	0	-1	10	-2

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Quadratic twists for elliptic curve 1147b1

-4	8	-3	5	-7	-31	37
18352i1	73408k1	10323e1	28675c1	56203b1	35557b1	42439b1

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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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