Cremona's table of elliptic curves

806 = 2 · 13 · 31

Field	Data	Notes
Atkin-Lehner	2- 13- 31+	Signs for the Atkin-Lehner involutions
Class	806c	Isogeny class
Conductor	806	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	160	Modular degree for the optimal curve
Δ	-399776 = -1 · 25 · 13 · 312	Discriminant
Eigenvalues	2-  1 -3 -3 -4 13-  3 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-97,361]	[a1,a2,a3,a4,a6]
Generators	[12:25:1]	Generators of the group modulo torsion
j	-100999381393/399776	j-invariant
L	3.0094615133551	L(r)(E,1)/r!
Ω	3.0117139374431	Real period
R	0.09992521122076	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6448l1 25792c1 7254e1 20150a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 806c1

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
-	1	-3	-3	-4	-	3	-4	-4	6	+	-5	-4	-1	5	8	4	-2	2	7	-14	-2	-6	-2	16

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Quadratic twists for elliptic curve 806c1

-4	8	-3	5	-7	-11	13	-31
6448l1	25792c1	7254e1	20150a1	39494u1	97526e1	10478f1	24986h1

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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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