Cremona's table of elliptic curves

174 = 2 · 3 · 29

Field	Data	Notes
Atkin-Lehner	2+ 3- 29+	Signs for the Atkin-Lehner involutions
Class	174a	Isogeny class
Conductor	174	Conductor
∏ cp	7	Product of Tamagawa factors cp
Δ	-458176313589497856 = -1 · 233 · 37 · 293	Discriminant
Eigenvalues	2+ 3- -3  5  6 -4  3 -1	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,68840,-31810330]	[a1,a2,a3,a4,a6]
j	36079072622241241607/458176313589497856	j-invariant
L	1.018019957343	L(r)(E,1)/r!
Ω	0.14543142247757	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1392i2 5568g2 522m2 4350q2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 174a2

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
+	-	-3	5	6	-4	3	-1	0	+	-4	-1	-9	-7	-3	-6	3	-10	-4	12	2	14	0	-6	8

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Quadratic twists for elliptic curve 174a2

-4	8	-3	5	-7	-11	13	17	-19	-23	29
1392i2	5568g2	522m2	4350q2	8526e2	21054bh2	29406v2	50286e2	62814p2	92046m2	5046i2

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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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