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	174b	Isogeny class
Conductor	174	Conductor
∏ cp	7	Product of Tamagawa factors cp
Δ	-103499257854 = -1 · 2 · 3 · 297	Discriminant
Eigenvalues	2- 3- -1  1 -2  0 -3 -1	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-6511,-203353]	[a1,a2,a3,a4,a6]
j	-30526075007211889/103499257854	j-invariant
L	1.8598039585135	L(r)(E,1)/r!
Ω	0.26568627978764	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	1392k2 5568b2 522d2 4350d2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 174b2

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
-	-	-1	1	-2	0	-3	-1	-4	-	4	3	-7	9	-1	-2	-3	6	12	16	-10	10	0	6	0

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Quadratic twists for elliptic curve 174b2

-4	8	-3	5	-7	-11	13	17	-19	-23	29
1392k2	5568b2	522d2	4350d2	8526o2	21054n2	29406i2	50286n2	62814d2	92046bf2	5046a2

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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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