Cremona's table of elliptic curves

2209 = 47²

Field	Data	Notes
Atkin-Lehner	47-	Signs for the Atkin-Lehner involutions
Class	2209b	Isogeny class
Conductor	2209	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	5640	Modular degree for the optimal curve
Δ	-23811286661761 = -1 · 478	Discriminant
Eigenvalues	-1  2 -3 -2 -6 -3  3 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,2163,232460]	[a1,a2,a3,a4,a6]
j	47	j-invariant
L	0.50441140933686	L(r)(E,1)/r!
Ω	0.50441140933686	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	35344e1 19881l1 55225f1 108241c1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2209b1

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
-1	2	-3	-2	-6	-3	3	-4	-2	2	6	6	10	6	-	5	0	-7	-8	-6	-10	14	4	11	-9

---

Quadratic twists for elliptic curve 2209b1

-4	-3	5	-7	-47
35344e1	19881l1	55225f1	108241c1	2209a1

---

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