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	48	Product of Tamagawa factors cp
deg	8448	Modular degree for the optimal curve
Δ	-39713884013808 = -1 · 24 · 36 · 237	Discriminant
Eigenvalues	2+ 3-  0 -2  0  2  0 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-18791,-1038310]	[a1,a2,a3,a4,a6]
Generators	[251:3048:1]	Generators of the group modulo torsion
j	-4956477625/268272	j-invariant
L	2.9011371124705	L(r)(E,1)/r!
Ω	0.20324526889413	Real period
R	1.189505799346	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	25392w1 101568e1 9522h1 79350cl1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3174d1

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 3174d1

-4	8	-3	5	-23
25392w1	101568e1	9522h1	79350cl1	138b1

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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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