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	4400v	Isogeny class
Conductor	4400	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	-11264000 = -1 · 213 · 53 · 11	Discriminant
Eigenvalues	2-  1 5- -3 11+  4  3  5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-448,3508]	[a1,a2,a3,a4,a6]
Generators	[18:40:1]	Generators of the group modulo torsion
j	-19465109/22	j-invariant
L	3.9859581362368	L(r)(E,1)/r!
Ω	2.2610916432387	Real period
R	0.22035584825564	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	550k1 17600dd1 39600fe1 4400w1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4400v1

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	-	-3	+	4	3	5	-4	5	-7	-7	-8	6	-8	9	0	-13	12	3	-6	0	-4	-15	-12

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Quadratic twists for elliptic curve 4400v1

-4	8	-3	5	-11
550k1	17600dd1	39600fe1	4400w1	48400cx1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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