Cremona's table of elliptic curves

22704 = 2⁴ · 3 · 11 · 43

Field	Data	Notes
Atkin-Lehner	2+ 3- 11+ 43-	Signs for the Atkin-Lehner involutions
Class	22704l	Isogeny class
Conductor	22704	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	249488262144 = 210 · 32 · 114 · 432	Discriminant
Eigenvalues	2+ 3- -2  4 11+ -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-5224,-145084]	[a1,a2,a3,a4,a6]
Generators	[1406:52668:1]	Generators of the group modulo torsion
j	15399846504868/243640881	j-invariant
L	6.3953694390032	L(r)(E,1)/r!
Ω	0.56209314010475	Real period
R	5.6888876439689	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	11352k2 90816by2 68112w2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 22704l2

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

---

Quadratic twists for elliptic curve 22704l2

-4	8	-3
11352k2	90816by2	68112w2

---

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