Cremona's table of elliptic curves

4485 = 3 · 5 · 13 · 23

Field	Data	Notes
Atkin-Lehner	3- 5+ 13+ 23-	Signs for the Atkin-Lehner involutions
Class	4485d	Isogeny class
Conductor	4485	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	480	Modular degree for the optimal curve
Δ	-4485 = -1 · 3 · 5 · 13 · 23	Discriminant
Eigenvalues	-1 3- 5+  1 -3 13+  6  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-66,201]	[a1,a2,a3,a4,a6]
Generators	[5:-1:1]	Generators of the group modulo torsion
j	-31824875809/4485	j-invariant
L	2.6799792036658	L(r)(E,1)/r!
Ω	4.2050249519102	Real period
R	0.63732777672304	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	71760v1 13455h1 22425e1 58305n1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 4485d1

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	+	6	0	-	-8	-7	-6	-9	10	7	6	-2	2	4	12	-1	9	12	-8	-16

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Quadratic twists for elliptic curve 4485d1

-4	-3	5	13	-23
71760v1	13455h1	22425e1	58305n1	103155j1

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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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