Cremona's table of elliptic curves

4400 = 2⁴ · 5² · 11

Field	Data	Notes
Atkin-Lehner	2+ 5- 11-	Signs for the Atkin-Lehner involutions
Class	4400i	Isogeny class
Conductor	4400	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	-2816000 = -1 · 211 · 53 · 11	Discriminant
Eigenvalues	2+ -1 5-  1 11-  0 -1 -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,32,32]	[a1,a2,a3,a4,a6]
Generators	[2:10:1]	Generators of the group modulo torsion
j	13718/11	j-invariant
L	3.1259197755798	L(r)(E,1)/r!
Ω	1.6415899563214	Real period
R	0.47605063669256	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	2200i1 17600cs1 39600bi1 4400h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4400i1

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	-	1	-	0	-1	-1	0	-1	1	-1	0	6	8	-9	-4	-7	-4	-5	-14	-4	16	-7	16

---

Quadratic twists for elliptic curve 4400i1

-4	8	-3	5	-11
2200i1	17600cs1	39600bi1	4400h1	48400w1

---

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