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	3162a	Isogeny class
Conductor	3162	Conductor
∏ cp	208	Product of Tamagawa factors cp
deg	79872	Modular degree for the optimal curve
Δ	-67059202299789312 = -1 · 226 · 38 · 173 · 31	Discriminant
Eigenvalues	2- 3-  4  4  0 -4 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-218011,-41131567]	[a1,a2,a3,a4,a6]
j	-1145932555163668707889/67059202299789312	j-invariant
L	5.7250851100643	L(r)(E,1)/r!
Ω	0.11009779057816	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	25296i1 101184g1 9486c1 79050g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3162a1

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	-8	-6	-	-2	-10	-6	8	-4	4	10	-16	-12	-6	0	14	10	-2

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Quadratic twists for elliptic curve 3162a1

-4	8	-3	5	17	-31
25296i1	101184g1	9486c1	79050g1	53754j1	98022s1

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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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