Cremona's table of elliptic curves

4508 = 2² · 7² · 23

Field	Data	Notes
Atkin-Lehner	2- 7- 23-	Signs for the Atkin-Lehner involutions
Class	4508d	Isogeny class
Conductor	4508	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	1728	Modular degree for the optimal curve
Δ	-43294832 = -1 · 24 · 76 · 23	Discriminant
Eigenvalues	2-  3  2 7-  2  5 -4  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-49,-343]	[a1,a2,a3,a4,a6]
j	-6912/23	j-invariant
L	4.9813821297622	L(r)(E,1)/r!
Ω	0.83023035496037	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	18032w1 72128z1 40572s1 112700j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4508d1

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
-	3	2	-	2	5	-4	2	-	-7	3	2	9	-8	-9	2	0	2	14	-3	3	-6	-8	-12	0

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Quadratic twists for elliptic curve 4508d1

-4	8	-3	5	-7	-23
18032w1	72128z1	40572s1	112700j1	92b1	103684j1

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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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