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	861c	Isogeny class
Conductor	861	Conductor
∏ cp	35	Product of Tamagawa factors cp
deg	2240	Modular degree for the optimal curve
Δ	-1773642581109 = -1 · 37 · 7 · 415	Discriminant
Eigenvalues	-1 3-  3 7+ -6 -7 -6 -6	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,2941,18606]	[a1,a2,a3,a4,a6]
Generators	[-5:64:1]	Generators of the group modulo torsion
j	2813193182704463/1773642581109	j-invariant
L	1.9612976332841	L(r)(E,1)/r!
Ω	0.51981235681085	Real period
R	0.10780250700558	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	13776k1 55104i1 2583c1 21525j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 861c1

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	-	3	+	-6	-7	-6	-6	5	3	0	1	-	6	-5	-9	-8	-2	9	-10	4	9	-2	16	13

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Quadratic twists for elliptic curve 861c1

-4	8	-3	5	-7	-11	41
13776k1	55104i1	2583c1	21525j1	6027b1	104181s1	35301f1

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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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