Cremona's table of elliptic curves

2040 = 2³ · 3 · 5 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5- 17-	Signs for the Atkin-Lehner involutions
Class	2040c	Isogeny class
Conductor	2040	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	3746786595840 = 210 · 316 · 5 · 17	Discriminant
Eigenvalues	2+ 3+ 5-  0  0 -2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-4000,-27140]	[a1,a2,a3,a4,a6]
Generators	[-43:252:1]	Generators of the group modulo torsion
j	6913728144004/3658971285	j-invariant
L	2.7548786021808	L(r)(E,1)/r!
Ω	0.63724581349106	Real period
R	4.3231019237123	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	4080o3 16320z3 6120r3 10200bg3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2040c3

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

---

Quadratic twists for elliptic curve 2040c3

-4	8	-3	5	-7	17
4080o3	16320z3	6120r3	10200bg3	99960be4	34680p4

---

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