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	16	Product of Tamagawa factors cp
Δ	12135225600 = 28 · 38 · 52 · 172	Discriminant
Eigenvalues	2+ 3+ 5-  0  0 -2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2300,42900]	[a1,a2,a3,a4,a6]
Generators	[-38:272:1]	Generators of the group modulo torsion
j	5258429611216/47403225	j-invariant
L	2.7548786021808	L(r)(E,1)/r!
Ω	1.2744916269821	Real period
R	2.1615509618562	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	4080o2 16320z2 6120r2 10200bg2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2040c2

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 2040c2

-4	8	-3	5	-7	17
4080o2	16320z2	6120r2	10200bg2	99960be2	34680p2

---

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