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	806a	Isogeny class
Conductor	806	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	80	Modular degree for the optimal curve
Δ	-399776 = -1 · 25 · 13 · 312	Discriminant
Eigenvalues	2+  1  1 -3  0 13+ -5 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-3,30]	[a1,a2,a3,a4,a6]
Generators	[6:12:1]	Generators of the group modulo torsion
j	-1771561/399776	j-invariant
L	1.9545918895053	L(r)(E,1)/r!
Ω	2.4438911359956	Real period
R	0.39989340374384	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	6448g1 25792q1 7254n1 20150o1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 806a1

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	1	-3	0	+	-5	-2	-2	-2	+	11	-6	-1	9	6	4	-14	4	-9	-10	-4	12	-4	-2

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Quadratic twists for elliptic curve 806a1

-4	8	-3	5	-7	-11	13	-31
6448g1	25792q1	7254n1	20150o1	39494m1	97526x1	10478j1	24986d1

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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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