Cremona's table of elliptic curves

2046 = 2 · 3 · 11 · 31

Field	Data	Notes
Atkin-Lehner	2+ 3+ 11- 31-	Signs for the Atkin-Lehner involutions
Class	2046c	Isogeny class
Conductor	2046	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	7488	Modular degree for the optimal curve
Δ	-2217684344832 = -1 · 213 · 38 · 113 · 31	Discriminant
Eigenvalues	2+ 3+  2 -1 11-  0 -5 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-59009,5493237]	[a1,a2,a3,a4,a6]
Generators	[161:365:1]	Generators of the group modulo torsion
j	-22724271869580547993/2217684344832	j-invariant
L	2.1555326437715	L(r)(E,1)/r!
Ω	0.78697121540578	Real period
R	0.45650391475036	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	16368t1 65472u1 6138m1 51150ck1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2046c1

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	-1	-	0	-5	-2	3	-8	-	5	-6	-9	4	-2	9	-6	3	-14	14	2	11	-18	17

---

Quadratic twists for elliptic curve 2046c1

-4	8	-3	5	-7	-11	-31
16368t1	65472u1	6138m1	51150ck1	100254y1	22506bd1	63426l1

---

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