Cremona's table of elliptic curves

4550 = 2 · 5² · 7 · 13

Field	Data	Notes
Atkin-Lehner	2- 5+ 7+ 13-	Signs for the Atkin-Lehner involutions
Class	4550t	Isogeny class
Conductor	4550	Conductor
∏ cp	70	Product of Tamagawa factors cp
deg	20160	Modular degree for the optimal curve
Δ	-5198102000000 = -1 · 27 · 56 · 7 · 135	Discriminant
Eigenvalues	2- -3 5+ 7+ -5 13-  4  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-555,109947]	[a1,a2,a3,a4,a6]
Generators	[9:-330:1]	Generators of the group modulo torsion
j	-1207949625/332678528	j-invariant
L	3.1889349549398	L(r)(E,1)/r!
Ω	0.6230569528607	Real period
R	0.073117254261958	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	36400cg1 40950bh1 182e1 31850bu1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4550t1

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
-	-3	+	+	-5	-	4	2	-5	4	1	-7	-9	12	7	4	-6	13	-11	0	-7	-17	-4	14	-5

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Quadratic twists for elliptic curve 4550t1

-4	-3	5	-7	13
36400cg1	40950bh1	182e1	31850bu1	59150s1

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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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