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	21	Product of Tamagawa factors cp
deg	1540	Modular degree for the optimal curve
Δ	-621261297432576 = -1 · 211 · 321 · 29	Discriminant
Eigenvalues	2+ 3- -3  5  6 -4  3 -1	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-7705,1226492]	[a1,a2,a3,a4,a6]
j	-50577879066661513/621261297432576	j-invariant
L	1.018019957343	L(r)(E,1)/r!
Ω	0.43629426743271	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	1392i1 5568g1 522m1 4350q1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 174a1

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 174a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29
1392i1	5568g1	522m1	4350q1	8526e1	21054bh1	29406v1	50286e1	62814p1	92046m1	5046i1

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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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