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	1	Product of Tamagawa factors cp
deg	128	Modular degree for the optimal curve
Δ	-1027 = -1 · 13 · 79	Discriminant
Eigenvalues	0 -2  0 -1  6 13-  0  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-213,1128]	[a1,a2,a3,a4,a6]
Generators	[36:203:1]	Generators of the group modulo torsion
j	-1073741824000/1027	j-invariant
L	1.5905299604663	L(r)(E,1)/r!
Ω	4.1290004932663	Real period
R	3.4668849440782	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	16432j1 65728g1 9243d1 25675c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1027a1

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 1027a1

-4	8	-3	5	-7	-11	13	-79
16432j1	65728g1	9243d1	25675c1	50323b1	124267c1	13351b1	81133c1

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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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