Cremona's table of elliptic curves

3162 = 2 · 3 · 17 · 31

Field	Data	Notes
Atkin-Lehner	2- 3- 17- 31+	Signs for the Atkin-Lehner involutions
Class	3162b	Isogeny class
Conductor	3162	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	704	Modular degree for the optimal curve
Δ	-170748 = -1 · 22 · 34 · 17 · 31	Discriminant
Eigenvalues	2- 3- -4  4  0 -4 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,5,-19]	[a1,a2,a3,a4,a6]
j	13651919/170748	j-invariant
L	3.1590816561419	L(r)(E,1)/r!
Ω	1.579540828071	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	25296l1 101184i1 9486a1 79050c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3162b1

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

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Quadratic twists for elliptic curve 3162b1

-4	8	-3	5	17	-31
25296l1	101184i1	9486a1	79050c1	53754l1	98022r1

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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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