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	24	Product of Tamagawa factors cp
Δ	8457586410348 = 22 · 33 · 238	Discriminant
Eigenvalues	2+ 3-  0 -2  0  2  0 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-304451,-64683358]	[a1,a2,a3,a4,a6]
Generators	[872:17814:1]	Generators of the group modulo torsion
j	21081759765625/57132	j-invariant
L	2.9011371124705	L(r)(E,1)/r!
Ω	0.20324526889413	Real period
R	2.3790115986921	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	25392w2 101568e2 9522h2 79350cl2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3174d2

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 3174d2

-4	8	-3	5	-23
25392w2	101568e2	9522h2	79350cl2	138b2

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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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