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	1040c	Isogeny class
Conductor	1040	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	128	Modular degree for the optimal curve
Δ	266240 = 212 · 5 · 13	Discriminant
Eigenvalues	2-  2 5+  4 -2 13+  2  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-16,0]	[a1,a2,a3,a4,a6]
j	117649/65	j-invariant
L	2.5425284450636	L(r)(E,1)/r!
Ω	2.5425284450636	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	65a1 4160s1 9360bx1 5200bb1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1040c1

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	+	4	-2	+	2	6	6	2	10	-2	-6	-10	-4	2	-6	2	4	-6	-6	12	16	2	-2

---

Quadratic twists for elliptic curve 1040c1

-4	8	-3	5	-7	-11	13
65a1	4160s1	9360bx1	5200bb1	50960cf1	125840by1	13520bc1

---

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