Cremona's table of elliptic curves

423 = 3² · 47

Field	Data	Notes
Atkin-Lehner	3+ 47+	Signs for the Atkin-Lehner involutions
Class	423g	Isogeny class
Conductor	423	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	32	Modular degree for the optimal curve
Δ	1269 = 33 · 47	Discriminant
Eigenvalues	-2 3+ -3  1  3  0  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-9,10]	[a1,a2,a3,a4,a6]
Generators	[1:1:1]	Generators of the group modulo torsion
j	2985984/47	j-invariant
L	0.96209150021194	L(r)(E,1)/r!
Ω	4.8510516053507	Real period
R	0.099163189601072	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	6768k1 27072c1 423d1 10575d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 423g1

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
-2	+	-3	1	3	0	0	-4	-7	1	0	-3	-10	-12	+	-2	6	14	-14	-6	-10	5	2	-2	9

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Quadratic twists for elliptic curve 423g1

-4	8	-3	5	-7	-11	13	17	-47
6768k1	27072c1	423d1	10575d1	20727h1	51183a1	71487f1	122247b1	19881d1

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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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