Cremona's table of elliptic curves

1040 = 2⁴ · 5 · 13

Field	Data	Notes
Atkin-Lehner	2- 5- 13-	Signs for the Atkin-Lehner involutions
Class	1040f	Isogeny class
Conductor	1040	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-292464640000 = -1 · 214 · 54 · 134	Discriminant
Eigenvalues	2-  0 5-  0  0 13-  2  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1067,29274]	[a1,a2,a3,a4,a6]
j	-32798729601/71402500	j-invariant
L	1.7280911161207	L(r)(E,1)/r!
Ω	0.86404555806033	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	130b4 4160j4 9360bl4 5200n4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1040f4

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	-	0	0	-	2	8	4	-2	4	6	10	0	-8	6	-8	-2	-4	12	10	8	-12	10	-14

---

Quadratic twists for elliptic curve 1040f4

-4	8	-3	5	-7	-11	13
130b4	4160j4	9360bl4	5200n4	50960s3	125840cd3	13520n4

---

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