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	4400x	Isogeny class
Conductor	4400	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	247808000 = 214 · 53 · 112	Discriminant
Eigenvalues	2-  2 5-  0 11+  2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1688,-26128]	[a1,a2,a3,a4,a6]
Generators	[76:528:1]	Generators of the group modulo torsion
j	1039509197/484	j-invariant
L	4.9670437962907	L(r)(E,1)/r!
Ω	0.74481281793652	Real period
R	1.6672121090947	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	550g2 17600di2 39600es2 4400y2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4400x2

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	-	0	+	2	-6	-4	-2	-10	8	-8	-2	0	2	0	12	-10	-6	0	-6	-12	16	18	12

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Quadratic twists for elliptic curve 4400x2

-4	8	-3	5	-11
550g2	17600di2	39600es2	4400y2	48400da2

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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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