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	806b	Isogeny class
Conductor	806	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	176	Modular degree for the optimal curve
Δ	-25585664 = -1 · 211 · 13 · 312	Discriminant
Eigenvalues	2+ -1 -1  1  2 13+  7 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,52,-176]	[a1,a2,a3,a4,a6]
Generators	[5:13:1]	Generators of the group modulo torsion
j	15087533111/25585664	j-invariant
L	1.4834831912095	L(r)(E,1)/r!
Ω	1.1144535358649	Real period
R	0.66556529432078	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	6448f1 25792p1 7254m1 20150m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 806b1

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	1	2	+	7	-4	-6	-2	+	-7	10	1	1	-14	-6	-8	-8	-1	-10	-14	6	-12	4

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Quadratic twists for elliptic curve 806b1

-4	8	-3	5	-7	-11	13	-31
6448f1	25792p1	7254m1	20150m1	39494l1	97526z1	10478l1	24986c1

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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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