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	805b	Isogeny class
Conductor	805	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-311181605 = -1 · 5 · 76 · 232	Discriminant
Eigenvalues	-1  0 5+ 7+  2  4 -6 -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-138,-1018]	[a1,a2,a3,a4,a6]
j	-288673724529/311181605	j-invariant
L	0.66840825933862	L(r)(E,1)/r!
Ω	0.66840825933862	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	12880p2 51520y2 7245m2 4025b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 805b2

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	0	+	+	2	4	-6	-8	-	10	10	8	-2	0	12	-4	14	-2	-4	8	0	6	-12	10	-2

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Quadratic twists for elliptic curve 805b2

-4	8	-3	5	-7	-11	-23
12880p2	51520y2	7245m2	4025b2	5635j2	97405e2	18515m2

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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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