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	4550j	Isogeny class
Conductor	4550	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	23105468750000000 = 27 · 516 · 7 · 132	Discriminant
Eigenvalues	2+  2 5+ 7- -4 13-  0 -6	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-140625,-18992875]	[a1,a2,a3,a4,a6]
Generators	[-5253:30287:27]	Generators of the group modulo torsion
j	19683218700810001/1478750000000	j-invariant
L	3.8025259148559	L(r)(E,1)/r!
Ω	0.2477088596431	Real period
R	7.6753934444141	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	36400bn2 40950er2 910k2 31850o2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4550j2

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	-6	2	6	-8	6	-8	-4	8	0	-10	-14	4	6	-10	16	0	-16	-14

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Quadratic twists for elliptic curve 4550j2

-4	-3	5	-7	13
36400bn2	40950er2	910k2	31850o2	59150bk2

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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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