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	174d	Isogeny class
Conductor	174	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	30276 = 22 · 32 · 292	Discriminant
Eigenvalues	2+ 3-  2  0 -4  6 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-20,-34]	[a1,a2,a3,a4,a6]
j	822656953/30276	j-invariant
L	1.1382223798819	L(r)(E,1)/r!
Ω	2.2764447597637	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	1392h2 5568e2 522k2 4350o2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 174d2

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	0	-4	6	-2	4	0	+	-4	-6	6	-12	-8	-6	8	10	-4	-8	2	4	0	14	18

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Quadratic twists for elliptic curve 174d2

-4	8	-3	5	-7	-11	13	17	-19	-23	29
1392h2	5568e2	522k2	4350o2	8526d2	21054bf2	29406u2	50286d2	62814o2	92046h2	5046h2

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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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