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	16	Product of Tamagawa factors cp
Δ	25372759231044 = 22 · 34 · 238	Discriminant
Eigenvalues	2- 3+ -2  0  0 -2 -2  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-9004,-226039]	[a1,a2,a3,a4,a6]
Generators	[45479:308433:343]	Generators of the group modulo torsion
j	545338513/171396	j-invariant
L	3.8470357162768	L(r)(E,1)/r!
Ω	0.50221184895923	Real period
R	7.660185087726	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	25392be2 101568x2 9522e2 79350y2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3174g2

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 3174g2

-4	8	-3	5	-23
25392be2	101568x2	9522e2	79350y2	138c2

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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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