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	4	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	-2775303 = -1 · 310 · 47	Discriminant
Eigenvalues	1 3- -2  0 -4 -2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-18,-81]	[a1,a2,a3,a4,a6]
Generators	[18:63:1]	Generators of the group modulo torsion
j	-912673/3807	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	2	Number of elements in the torsion subgroup
Twists	6768p1 27072bd1 141c1 10575h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 423c1

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 423c1

-4	8	-3	5	-7	-11	13	17	-47
6768p1	27072bd1	141c1	10575h1	20727k1	51183i1	71487j1	122247q1	19881k1

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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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