Cremona's table of elliptic curves

423 = 3² · 47

Field	Data	Notes
Atkin-Lehner	3- 47-	Signs for the Atkin-Lehner involutions
Class	423c	Isogeny class
Conductor	423	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	102789 = 37 · 47	Discriminant
Eigenvalues	1 3- -2  0 -4 -2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-6768,-212625]	[a1,a2,a3,a4,a6]
Generators	[13734:561393:8]	Generators of the group modulo torsion
j	47034153084673/141	j-invariant
L	2.0430649787699	L(r)(E,1)/r!
Ω	0.52635828034344	Real period
R	7.7630201901141	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6768p4 27072bd4 141c4 10575h3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 423c3

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	0	-4	-2	-2	0	0	6	-4	-10	2	8	-	2	4	14	-8	-16	2	8	4	-18	-14

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Quadratic twists for elliptic curve 423c3

-4	8	-3	5	-7	-11	13	17	-47
6768p4	27072bd4	141c4	10575h3	20727k4	51183i4	71487j4	122247q4	19881k4

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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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