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	3174d	Isogeny class
Conductor	3174	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-66397691712172032 = -1 · 212 · 32 · 239	Discriminant
Eigenvalues	2+ 3-  0 -2  0  2  0 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,100234,-2114296]	[a1,a2,a3,a4,a6]
Generators	[47988:1399513:64]	Generators of the group modulo torsion
j	752329532375/448524288	j-invariant
L	2.9011371124705	L(r)(E,1)/r!
Ω	0.20324526889413	Real period
R	3.5685173980381	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	25392w3 101568e3 9522h3 79350cl3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3174d3

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
+	-	0	-2	0	2	0	-2	-	-6	-4	10	-6	-2	0	-12	12	10	-14	0	2	10	0	-12	10

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Quadratic twists for elliptic curve 3174d3

-4	8	-3	5	-23
25392w3	101568e3	9522h3	79350cl3	138b3

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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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