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	1040g	Isogeny class
Conductor	1040	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	106496000 = 216 · 53 · 13	Discriminant
Eigenvalues	2-  2 5-  4  6 13- -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-520,-4368]	[a1,a2,a3,a4,a6]
j	3803721481/26000	j-invariant
L	3.0000554918468	L(r)(E,1)/r!
Ω	1.0000184972823	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	130a1 4160n1 9360br1 5200s1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1040g1

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	6	-	-6	-2	-6	-6	-2	2	-6	-2	12	6	-6	2	4	6	-10	4	0	-6	2

---

Quadratic twists for elliptic curve 1040g1

-4	8	-3	5	-7	-11	13
130a1	4160n1	9360br1	5200s1	50960y1	125840ck1	13520t1

---

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