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	1040a	Isogeny class
Conductor	1040	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	4326400 = 210 · 52 · 132	Discriminant
Eigenvalues	2+  0 5+  0  4 13+ -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-43,42]	[a1,a2,a3,a4,a6]
Generators	[-3:12:1]	Generators of the group modulo torsion
j	8586756/4225	j-invariant
L	2.3676351838733	L(r)(E,1)/r!
Ω	2.1816867292797	Real period
R	1.0852315101421	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	520a2 4160o2 9360r2 5200e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1040a2

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	4	+	-6	-4	0	-2	4	-6	-6	-8	0	2	-4	-10	-12	4	14	16	-12	2	-2

---

Quadratic twists for elliptic curve 1040a2

-4	8	-3	5	-7	-11	13
520a2	4160o2	9360r2	5200e2	50960j2	125840i2	13520h2

---

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