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	861d	Isogeny class
Conductor	861	Conductor
∏ cp	5	Product of Tamagawa factors cp
deg	80	Modular degree for the optimal curve
Δ	-69741 = -1 · 35 · 7 · 41	Discriminant
Eigenvalues	-1 3- -3 7- -2  5 -2 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-7,14]	[a1,a2,a3,a4,a6]
Generators	[-1:5:1]	Generators of the group modulo torsion
j	-38272753/69741	j-invariant
L	1.6446967712049	L(r)(E,1)/r!
Ω	3.0961653380118	Real period
R	0.10624088778548	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	13776f1 55104o1 2583f1 21525c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 861d1

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	-	-2	5	-2	-2	-3	1	-8	1	+	-10	-9	-11	-4	2	-5	-6	4	11	14	8	1

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Quadratic twists for elliptic curve 861d1

-4	8	-3	5	-7	-11	41
13776f1	55104o1	2583f1	21525c1	6027d1	104181p1	35301b1

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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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