Cremona's table of elliptic curves

3174 = 2 · 3 · 23²

Field	Data	Notes
Atkin-Lehner	2+ 3- 23-	Signs for the Atkin-Lehner involutions
Class	3174d	Isogeny class
Conductor	3174	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	4207607890947901632 = 26 · 3 · 2312	Discriminant
Eigenvalues	2+ 3-  0 -2  0  2  0 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-407606,-17146360]	[a1,a2,a3,a4,a6]
Generators	[-102414:1852873:216]	Generators of the group modulo torsion
j	50591419971625/28422890688	j-invariant
L	2.9011371124705	L(r)(E,1)/r!
Ω	0.20324526889413	Real period
R	7.1370347960762	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	25392w4 101568e4 9522h4 79350cl4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3174d4

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	-2	0	2	0	-2	-	-6	-4	10	-6	-2	0	-12	12	10	-14	0	2	10	0	-12	10

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Quadratic twists for elliptic curve 3174d4

-4	8	-3	5	-23
25392w4	101568e4	9522h4	79350cl4	138b4

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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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