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	16	Product of Tamagawa factors cp
Δ	10671862347 = 37 · 474	Discriminant
Eigenvalues	1 3- -2  0 -4 -2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-558,-891]	[a1,a2,a3,a4,a6]
Generators	[-12:69:1]	Generators of the group modulo torsion
j	26383748833/14639043	j-invariant
L	2.0430649787699	L(r)(E,1)/r!
Ω	1.0527165606869	Real period
R	1.9407550475285	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	6768p3 27072bd3 141c3 10575h4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 423c4

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 423c4

-4	8	-3	5	-7	-11	13	17	-47
6768p3	27072bd3	141c3	10575h4	20727k3	51183i3	71487j3	122247q3	19881k3

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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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