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	4400g	Isogeny class
Conductor	4400	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	640	Modular degree for the optimal curve
Δ	-352000 = -1 · 28 · 53 · 11	Discriminant
Eigenvalues	2+ -2 5- -4 11+ -6  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,12,28]	[a1,a2,a3,a4,a6]
Generators	[-1:4:1] [2:8:1]	Generators of the group modulo torsion
j	5488/11	j-invariant
L	3.292478646049	L(r)(E,1)/r!
Ω	2.0929398815341	Real period
R	1.5731357957763	Regulator
r	2	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2200k1 17600dg1 39600bu1 4400f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4400g1

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	-	-4	+	-6	2	-4	-6	-2	-8	-8	6	-12	-10	0	4	-10	-2	8	2	-4	4	-14	-4

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Quadratic twists for elliptic curve 4400g1

-4	8	-3	5	-11
2200k1	17600dg1	39600bu1	4400f1	48400be1

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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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