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	8	Product of Tamagawa factors cp
Δ	14493249 = 38 · 472	Discriminant
Eigenvalues	1 3- -2  0 -4 -2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-423,-3240]	[a1,a2,a3,a4,a6]
Generators	[1716:70206:1]	Generators of the group modulo torsion
j	11497268593/19881	j-invariant
L	2.0430649787699	L(r)(E,1)/r!
Ω	1.0527165606869	Real period
R	3.8815100950571	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	6768p2 27072bd2 141c2 10575h2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 423c2

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 423c2

-4	8	-3	5	-7	-11	13	17	-47
6768p2	27072bd2	141c2	10575h2	20727k2	51183i2	71487j2	122247q2	19881k2

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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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