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	4550i	Isogeny class
Conductor	4550	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1920	Modular degree for the optimal curve
Δ	-1119591200 = -1 · 25 · 52 · 72 · 134	Discriminant
Eigenvalues	2+ -1 5+ 7- -1 13- -3 -3	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-175,-1915]	[a1,a2,a3,a4,a6]
Generators	[19:36:1]	Generators of the group modulo torsion
j	-23920470625/44783648	j-invariant
L	2.2502285461478	L(r)(E,1)/r!
Ω	0.61774195905127	Real period
R	0.45533343517812	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	36400bm1 40950ei1 4550v1 31850f1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4550i1

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
+	-1	+	-	-1	-	-3	-3	8	6	-8	0	-5	8	2	0	-4	10	-5	-6	-1	-14	-3	5	-14

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Quadratic twists for elliptic curve 4550i1

-4	-3	5	-7	13
36400bm1	40950ei1	4550v1	31850f1	59150bj1

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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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