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	1040b	Isogeny class
Conductor	1040	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	64	Modular degree for the optimal curve
Δ	16640 = 28 · 5 · 13	Discriminant
Eigenvalues	2+ -2 5-  0 -2 13-  2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-20,28]	[a1,a2,a3,a4,a6]
Generators	[-2:8:1]	Generators of the group modulo torsion
j	3631696/65	j-invariant
L	1.9560341447686	L(r)(E,1)/r!
Ω	3.9107191914199	Real period
R	1.0003449744283	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	520b1 4160m1 9360k1 5200b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1040b1

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

---

Quadratic twists for elliptic curve 1040b1

-4	8	-3	5	-7	-11	13
520b1	4160m1	9360k1	5200b1	50960a1	125840u1	13520e1

---

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