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	4550s	Isogeny class
Conductor	4550	Conductor
∏ cp	160	Product of Tamagawa factors cp
deg	23040	Modular degree for the optimal curve
Δ	1304576000000000 = 220 · 59 · 72 · 13	Discriminant
Eigenvalues	2-  0 5+ 7+  4 13- -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-50005,3949997]	[a1,a2,a3,a4,a6]
Generators	[-241:1520:1]	Generators of the group modulo torsion
j	884984855328729/83492864000	j-invariant
L	5.2832102690804	L(r)(E,1)/r!
Ω	0.46997937663967	Real period
R	1.1241366178352	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	36400cd1 40950bg1 910a1 31850bs1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4550s1

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	-	-2	-4	-8	-2	4	-10	-6	0	-8	-2	12	-2	4	12	2	-8	-4	2	-14

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Quadratic twists for elliptic curve 4550s1

-4	-3	5	-7	13
36400cd1	40950bg1	910a1	31850bs1	59150h1

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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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