Cremona's table of elliptic curves

854 = 2 · 7 · 61

Field	Data	Notes
Atkin-Lehner	2- 7- 61+	Signs for the Atkin-Lehner involutions
Class	854d	Isogeny class
Conductor	854	Conductor
∏ cp	42	Product of Tamagawa factors cp
deg	336	Modular degree for the optimal curve
Δ	3215111872 = 26 · 77 · 61	Discriminant
Eigenvalues	2- -1 -2 7-  1 -4 -1 -5	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-399,1237]	[a1,a2,a3,a4,a6]
Generators	[-19:58:1]	Generators of the group modulo torsion
j	7026036894577/3215111872	j-invariant
L	2.6429141568418	L(r)(E,1)/r!
Ω	1.2693965421916	Real period
R	0.04957200169713	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	6832c1 27328k1 7686j1 21350a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 854d1

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	-	1	-4	-1	-5	-3	2	-2	-2	-12	-1	-5	0	4	+	3	-3	-4	1	7	7	-2

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Quadratic twists for elliptic curve 854d1

-4	8	-3	5	-7	-11	61
6832c1	27328k1	7686j1	21350a1	5978l1	103334g1	52094a1

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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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