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
Δ	15391887429869568 = 213 · 34 · 176 · 312	Discriminant
Eigenvalues	2- 3-  4  4  0 -4 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-3535771,-2559311407]	[a1,a2,a3,a4,a6]
j	4888505500429076644231729/15391887429869568	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	25296i2 101184g2 9486c2 79050g2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3162a2

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 3162a2

-4	8	-3	5	17	-31
25296i2	101184g2	9486c2	79050g2	53754j2	98022s2

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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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