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	861a	Isogeny class
Conductor	861	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	59340981 = 3 · 7 · 414	Discriminant
Eigenvalues	-1 3+  2 7-  0  2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-147,516]	[a1,a2,a3,a4,a6]
j	351447414193/59340981	j-invariant
L	0.94298550013938	L(r)(E,1)/r!
Ω	1.8859710002788	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	13776o3 55104bk3 2583e3 21525v3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 861a4

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

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Quadratic twists for elliptic curve 861a4

-4	8	-3	5	-7	-11	41
13776o3	55104bk3	2583e3	21525v3	6027h3	104181e3	35301h3

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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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