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	174c	Isogeny class
Conductor	174	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	12	Modular degree for the optimal curve
Δ	-1566 = -1 · 2 · 33 · 29	Discriminant
Eigenvalues	2- 3+  1  1  6 -4 -7 -3	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-5,-7]	[a1,a2,a3,a4,a6]
j	-13997521/1566	j-invariant
L	1.5847007716704	L(r)(E,1)/r!
Ω	1.5847007716704	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	1392m1 5568m1 522e1 4350j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 174c1

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	6	-4	-7	-3	4	+	0	-7	5	-5	-5	10	3	10	0	-4	10	-6	16	-10	-8

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Quadratic twists for elliptic curve 174c1

-4	8	-3	5	-7	-11	13	17	-19	-23	29
1392m1	5568m1	522e1	4350j1	8526w1	21054f1	29406b1	50286s1	62814i1	92046v1	5046d1

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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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