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	24	Product of Tamagawa factors cp
deg	23040	Modular degree for the optimal curve
Δ	-949731328000000 = -1 · 220 · 56 · 73 · 132	Discriminant
Eigenvalues	2+  0 5+ 7-  4 13-  6  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,21658,827316]	[a1,a2,a3,a4,a6]
Generators	[189:3318:1]	Generators of the group modulo torsion
j	71903073502287/60782804992	j-invariant
L	2.8918237505421	L(r)(E,1)/r!
Ω	0.32148750244085	Real period
R	1.4991893041908	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	36400bk1 40950ev1 182a1 31850e1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4550h1

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 4550h1

-4	-3	5	-7	13
36400bk1	40950ev1	182a1	31850e1	59150be1

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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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