Cremona's table of elliptic curves

861 = 3 · 7 · 41

Field	Data	Notes
Atkin-Lehner	3- 7+ 41-	Signs for the Atkin-Lehner involutions
Class	861b	Isogeny class
Conductor	861	Conductor
∏ cp	17	Product of Tamagawa factors cp
deg	1632	Modular degree for the optimal curve
Δ	-1816098112269 = -1 · 317 · 73 · 41	Discriminant
Eigenvalues	1 3- -1 7+ -6  3 -6  6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,706,-64375]	[a1,a2,a3,a4,a6]
Generators	[45:220:1]	Generators of the group modulo torsion
j	38996155237031/1816098112269	j-invariant
L	2.9817201837828	L(r)(E,1)/r!
Ω	0.40044253928812	Real period
R	0.43800367773166	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	13776i1 55104e1 2583d1 21525l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 861b1

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	+	-6	3	-6	6	-9	5	-8	-7	-	2	3	9	-12	6	13	-6	4	-11	2	-4	-9

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Quadratic twists for elliptic curve 861b1

-4	8	-3	5	-7	-11	41
13776i1	55104e1	2583d1	21525l1	6027a1	104181t1	35301c1

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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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