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	4550r	Isogeny class
Conductor	4550	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-577636718750 = -1 · 2 · 512 · 7 · 132	Discriminant
Eigenvalues	2-  0 5+ 7+ -2 13-  4 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,1020,-34603]	[a1,a2,a3,a4,a6]
Generators	[310:1833:8]	Generators of the group modulo torsion
j	7518017079/36968750	j-invariant
L	5.1360748826747	L(r)(E,1)/r!
Ω	0.46275679092143	Real period
R	5.5494322108681	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	36400cc2 40950be2 910d2 31850br2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4550r2

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	+	+	-2	-	4	-4	4	-2	-2	2	0	-6	-8	4	-12	-2	-8	-12	2	-8	-4	-16	-2

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Quadratic twists for elliptic curve 4550r2

-4	-3	5	-7	13
36400cc2	40950be2	910d2	31850br2	59150g2

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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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