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	2	Product of Tamagawa factors cp
deg	10	Modular degree for the optimal curve
Δ	-1392 = -1 · 24 · 3 · 29	Discriminant
Eigenvalues	2+ 3-  2  0 -4  6 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,0,-2]	[a1,a2,a3,a4,a6]
j	12167/1392	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	2	Number of elements in the torsion subgroup
Twists	1392h1 5568e1 522k1 4350o1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 174d1

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 174d1

-4	8	-3	5	-7	-11	13	17	-19	-23	29
1392h1	5568e1	522k1	4350o1	8526d1	21054bf1	29406u1	50286d1	62814o1	92046h1	5046h1

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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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