Cremona's table of elliptic curves

423 = 3² · 47

Field	Data	Notes
Atkin-Lehner	3- 47-	Signs for the Atkin-Lehner involutions
Class	423a	Isogeny class
Conductor	423	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	32	Modular degree for the optimal curve
Δ	102789 = 37 · 47	Discriminant
Eigenvalues	0 3-  1 -3  3 -4 -8 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-12,4]	[a1,a2,a3,a4,a6]
Generators	[-2:4:1]	Generators of the group modulo torsion
j	262144/141	j-invariant
L	1.6367929760762	L(r)(E,1)/r!
Ω	2.9332316211672	Real period
R	0.13950423862409	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6768n1 27072bb1 141d1 10575g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 423a1

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
0	-	1	-3	3	-4	-8	-6	-3	1	4	1	10	-8	-	-10	10	2	4	6	-8	-3	18	2	5

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Quadratic twists for elliptic curve 423a1

-4	8	-3	5	-7	-11	13	17	-47
6768n1	27072bb1	141d1	10575g1	20727j1	51183g1	71487g1	122247l1	19881e1

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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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