Cremona's table of elliptic curves

3174 = 2 · 3 · 23²

Field	Data	Notes
Atkin-Lehner	2- 3+ 23-	Signs for the Atkin-Lehner involutions
Class	3174g	Isogeny class
Conductor	3174	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	745677201845682 = 2 · 32 · 2310	Discriminant
Eigenvalues	2- 3+ -2  0  0 -2 -2  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-56614,4992017]	[a1,a2,a3,a4,a6]
Generators	[-402:22415:8]	Generators of the group modulo torsion
j	135559106353/5037138	j-invariant
L	3.8470357162768	L(r)(E,1)/r!
Ω	0.50221184895923	Real period
R	3.830092543863	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	25392be3 101568x3 9522e3 79350y3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3174g4

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	0	-2	-2	8	-	-2	-8	-2	10	-8	8	-2	-4	-2	-8	0	-6	-8	16	-18	-10

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Quadratic twists for elliptic curve 3174g4

-4	8	-3	5	-23
25392be3	101568x3	9522e3	79350y3	138c3

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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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