Cremona's table of elliptic curves

805 = 5 · 7 · 23

Field	Data	Notes
Atkin-Lehner	5+ 7+ 23+	Signs for the Atkin-Lehner involutions
Class	805a	Isogeny class
Conductor	805	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	5720	Modular degree for the optimal curve
Δ	-3268768272021875 = -1 · 55 · 711 · 232	Discriminant
Eigenvalues	2 -1 5+ 7+ -5  3 -5  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,23004,2393001]	[a1,a2,a3,a4,a6]
Generators	[362:15015:8]	Generators of the group modulo torsion
j	1346216501445963776/3268768272021875	j-invariant
L	3.2924658901195	L(r)(E,1)/r!
Ω	0.31217463854874	Real period
R	5.2734358970122	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	12880t1 51520t1 7245q1 4025e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 805a1

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
2	-1	+	+	-5	3	-5	0	+	3	6	-4	0	-2	-9	-6	-6	10	4	-8	10	-15	12	-10	7

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Quadratic twists for elliptic curve 805a1

-4	8	-3	5	-7	-11	-23
12880t1	51520t1	7245q1	4025e1	5635g1	97405c1	18515t1

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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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