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	1640d	Isogeny class
Conductor	1640	Conductor
∏ cp	60	Product of Tamagawa factors cp
deg	4800	Modular degree for the optimal curve
Δ	689210000000000 = 210 · 510 · 413	Discriminant
Eigenvalues	2+  0 5-  2 -2 -2 -4 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-31307,-1717706]	[a1,a2,a3,a4,a6]
Generators	[663:16400:1]	Generators of the group modulo torsion
j	3313966509875844/673056640625	j-invariant
L	2.9729729362591	L(r)(E,1)/r!
Ω	0.36402721220813	Real period
R	0.54445983460513	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	3280g1 13120i1 14760o1 8200j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1640d1

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

---

Quadratic twists for elliptic curve 1640d1

-4	8	-3	5	-7	41
3280g1	13120i1	14760o1	8200j1	80360a1	67240c1

---

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