Cremona's table of elliptic curves

1640 = 2³ · 5 · 41

Field	Data	Notes
Atkin-Lehner	2+ 5- 41+	Signs for the Atkin-Lehner involutions
Class	1640b	Isogeny class
Conductor	1640	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	262400 = 28 · 52 · 41	Discriminant
Eigenvalues	2+  2 5-  2 -4  4  4  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-220,1332]	[a1,a2,a3,a4,a6]
j	4620876496/1025	j-invariant
L	3.021685461043	L(r)(E,1)/r!
Ω	3.021685461043	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	3280d2 13120f2 14760r2 8200h2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1640b2

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

---

Quadratic twists for elliptic curve 1640b2

-4	8	-3	5	-7	41
3280d2	13120f2	14760r2	8200h2	80360e2	67240f2

---

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