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	-837755450467 = -1 · 139 · 79	Discriminant
Eigenvalues	0 -2  0 -1  6 13-  0  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,1417,-38490]	[a1,a2,a3,a4,a6]
Generators	[52:422:1]	Generators of the group modulo torsion
j	314432000000000/837755450467	j-invariant
L	1.5905299604663	L(r)(E,1)/r!
Ω	0.45877783258515	Real period
R	0.38520943823091	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	16432j3 65728g3 9243d3 25675c3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1027a3

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

---

Quadratic twists for elliptic curve 1027a3

-4	8	-3	5	-7	-11	13	-79
16432j3	65728g3	9243d3	25675c3	50323b3	124267c3	13351b3	81133c3

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations