Cremona's table of elliptic curves

1014 = 2 · 3 · 13²

Field	Data	Notes
Atkin-Lehner	2- 3- 13+	Signs for the Atkin-Lehner involutions
Class	1014f	Isogeny class
Conductor	1014	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	-31539456 = -1 · 28 · 36 · 132	Discriminant
Eigenvalues	2- 3- -3 -2 -6 13+ -3 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-62,324]	[a1,a2,a3,a4,a6]
Generators	[4:10:1]	Generators of the group modulo torsion
j	-156116857/186624	j-invariant
L	3.3149785458493	L(r)(E,1)/r!
Ω	1.8855913051959	Real period
R	0.036626204654328	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	8112v1 32448i1 3042e1 25350e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1014f1

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
-	-	-3	-2	-6	+	-3	-2	-6	3	4	7	3	-10	-6	3	0	-7	10	-6	13	-4	6	-18	-14

---

Quadratic twists for elliptic curve 1014f1

-4	8	-3	5	-7	-11	13
8112v1	32448i1	3042e1	25350e1	49686ck1	122694bm1	1014b1

---

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