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	4400w	Isogeny class
Conductor	4400	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-41229056000000000 = -1 · 217 · 59 · 115	Discriminant
Eigenvalues	2- -1 5-  3 11+ -4 -3  5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,78792,-4819088]	[a1,a2,a3,a4,a6]
Generators	[1042:34750:1]	Generators of the group modulo torsion
j	6761990971/5153632	j-invariant
L	3.2152348336021	L(r)(E,1)/r!
Ω	0.20223818470554	Real period
R	3.9745644946866	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	550f2 17600dc2 39600fb2 4400v2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4400w2

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 4400w2

-4	8	-3	5	-11
550f2	17600dc2	39600fb2	4400v2	48400cz2

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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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