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	4400b	Isogeny class
Conductor	4400	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	3781250000 = 24 · 59 · 112	Discriminant
Eigenvalues	2+  0 5+ -2 11-  0  0  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-950,10875]	[a1,a2,a3,a4,a6]
j	379275264/15125	j-invariant
L	1.3856158546182	L(r)(E,1)/r!
Ω	1.3856158546182	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2200e1 17600bm1 39600j1 880b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4400b1

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	+	-2	-	0	0	8	-8	10	-8	10	-2	-6	-8	-14	4	10	4	0	8	4	10	6	10

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Quadratic twists for elliptic curve 4400b1

-4	8	-3	5	-11
2200e1	17600bm1	39600j1	880b1	48400i1

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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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