Cremona's table of elliptic curves

4422 = 2 · 3 · 11 · 67

Field	Data	Notes
Atkin-Lehner	2- 3+ 11- 67+	Signs for the Atkin-Lehner involutions
Class	4422k	Isogeny class
Conductor	4422	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	7680	Modular degree for the optimal curve
Δ	786372820992 = 216 · 35 · 11 · 672	Discriminant
Eigenvalues	2- 3+  0 -4 11-  0  6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-5773,-165757]	[a1,a2,a3,a4,a6]
Generators	[-47:90:1]	Generators of the group modulo torsion
j	21278111797932625/786372820992	j-invariant
L	4.2871946496226	L(r)(E,1)/r!
Ω	0.54895297004985	Real period
R	0.97622084302444	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	35376v1 13266c1 110550v1 48642a1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4422k1

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

---

Quadratic twists for elliptic curve 4422k1

-4	-3	5	-11
35376v1	13266c1	110550v1	48642a1

---

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