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	4550m	Isogeny class
Conductor	4550	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	9242187500 = 22 · 59 · 7 · 132	Discriminant
Eigenvalues	2+  2 5- 7-  2 13- -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-18700,976500]	[a1,a2,a3,a4,a6]
j	370300910741/4732	j-invariant
L	2.3619582504486	L(r)(E,1)/r!
Ω	1.1809791252243	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	36400co2 40950fk2 4550w2 31850bl2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4550m2

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

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Quadratic twists for elliptic curve 4550m2

-4	-3	5	-7	13
36400co2	40950fk2	4550w2	31850bl2	59150cd2

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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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