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	4550h	Isogeny class
Conductor	4550	Conductor
∏ cp	96	Product of Tamagawa factors cp
Δ	139897818651500000 = 25 · 56 · 73 · 138	Discriminant
Eigenvalues	2+  0 5+ 7-  4 13-  6  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-1478342,691983316]	[a1,a2,a3,a4,a6]
Generators	[729:773:1]	Generators of the group modulo torsion
j	22868021811807457713/8953460393696	j-invariant
L	2.8918237505421	L(r)(E,1)/r!
Ω	0.32148750244085	Real period
R	0.3747973260477	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	36400bk4 40950ev4 182a4 31850e4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4550h4

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
+	0	+	-	4	-	6	0	-8	-10	-8	-6	-6	-4	8	-6	8	10	-4	-8	-2	8	0	18	-2

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Quadratic twists for elliptic curve 4550h4

-4	-3	5	-7	13
36400bk4	40950ev4	182a4	31850e4	59150be4

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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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