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	4550x	Isogeny class
Conductor	4550	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	5096000 = 26 · 53 · 72 · 13	Discriminant
Eigenvalues	2- -2 5- 7+ -4 13+  0  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-53,97]	[a1,a2,a3,a4,a6]
Generators	[-2:15:1]	Generators of the group modulo torsion
j	131872229/40768	j-invariant
L	3.6838427859972	L(r)(E,1)/r!
Ω	2.2451706790467	Real period
R	0.27346419735309	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	36400ct1 40950bz1 4550n1 31850cq1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4550x1

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

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Quadratic twists for elliptic curve 4550x1

-4	-3	5	-7	13
36400ct1	40950bz1	4550n1	31850cq1	59150bb1

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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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