Cremona's table of elliptic curves

1162 = 2 · 7 · 83

Field	Data	Notes
Atkin-Lehner	2+ 7+ 83+	Signs for the Atkin-Lehner involutions
Class	1162a	Isogeny class
Conductor	1162	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	144	Modular degree for the optimal curve
Δ	-56938 = -1 · 2 · 73 · 83	Discriminant
Eigenvalues	2+  2 -2 7+  1 -2 -6  1	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-21,-49]	[a1,a2,a3,a4,a6]
Generators	[5:-1:1]	Generators of the group modulo torsion
j	-1102302937/56938	j-invariant
L	2.3142806063892	L(r)(E,1)/r!
Ω	1.1049707404506	Real period
R	2.0944270483085	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	9296c1 37184d1 10458u1 29050n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1162a1

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	-2	+	1	-2	-6	1	4	-6	7	-8	-6	-4	0	-11	-6	5	-16	7	11	15	+	-17	6

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Quadratic twists for elliptic curve 1162a1

-4	8	-3	5	-7	-83
9296c1	37184d1	10458u1	29050n1	8134b1	96446e1

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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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