Cremona's table of elliptic curves

5640 = 2³ · 3 · 5 · 47

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 47-	Signs for the Atkin-Lehner involutions
Class	5640c	Isogeny class
Conductor	5640	Conductor
∏ cp	20	Product of Tamagawa factors cp
Δ	-1678119596513280 = -1 · 211 · 320 · 5 · 47	Discriminant
Eigenvalues	2+ 3- 5+ -4  4 -2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-9656,-2007696]	[a1,a2,a3,a4,a6]
Generators	[295:4572:1]	Generators of the group modulo torsion
j	-48621741154418/819394334235	j-invariant
L	4.0371425168825	L(r)(E,1)/r!
Ω	0.20322340997164	Real period
R	3.9731077413235	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	11280b4 45120t3 16920p4 28200u3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5640c4

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

---

Quadratic twists for elliptic curve 5640c4

-4	8	-3	5
11280b4	45120t3	16920p4	28200u3

---

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