Cremona's table of elliptic curves

4505 = 5 · 17 · 53

Field	Data	Notes
Atkin-Lehner	5- 17- 53-	Signs for the Atkin-Lehner involutions
Class	4505b	Isogeny class
Conductor	4505	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	6336	Modular degree for the optimal curve
Δ	2095909015625 = 56 · 17 · 534	Discriminant
Eigenvalues	1  2 5-  2  6  2 17-  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-4597,95784]	[a1,a2,a3,a4,a6]
j	10747187598081241/2095909015625	j-invariant
L	4.6998381653583	L(r)(E,1)/r!
Ω	0.78330636089306	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	72080j1 40545e1 22525a1 76585a1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 4505b1

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	2	-	2	6	2	-	0	-2	2	6	2	-2	-12	4	-	0	-2	8	6	-2	2	4	6	18

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Quadratic twists for elliptic curve 4505b1

-4	-3	5	17
72080j1	40545e1	22525a1	76585a1

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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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