Cremona's table of elliptic curves

1027 = 13 · 79

Field	Data	Notes
Atkin-Lehner	13- 79-	Signs for the Atkin-Lehner involutions
Class	1027a	Isogeny class
Conductor	1027	Conductor
∏ cp	9	Product of Tamagawa factors cp
Δ	-1083206683 = -1 · 133 · 793	Discriminant
Eigenvalues	0 -2  0 -1  6 13-  0  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-163,1721]	[a1,a2,a3,a4,a6]
Generators	[5:32:1]	Generators of the group modulo torsion
j	-481890304000/1083206683	j-invariant
L	1.5905299604663	L(r)(E,1)/r!
Ω	1.3763334977554	Real period
R	1.1556283146927	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	16432j2 65728g2 9243d2 25675c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1027a2

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	-2	0	-1	6	-	0	2	-9	6	-4	2	-3	-10	-3	-6	12	-10	14	0	-16	-	6	0	-10

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Quadratic twists for elliptic curve 1027a2

-4	8	-3	5	-7	-11	13	-79
16432j2	65728g2	9243d2	25675c2	50323b2	124267c2	13351b2	81133c2

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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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