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	854c	Isogeny class
Conductor	854	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	64	Modular degree for the optimal curve
Δ	109312 = 28 · 7 · 61	Discriminant
Eigenvalues	2- -1  0 7+ -5  0 -3 -1	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-13,3]	[a1,a2,a3,a4,a6]
Generators	[-1:4:1]	Generators of the group modulo torsion
j	244140625/109312	j-invariant
L	2.7291045756858	L(r)(E,1)/r!
Ω	2.9994943944001	Real period
R	0.11373185847509	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	6832k1 27328a1 7686f1 21350h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 854c1

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	0	+	-5	0	-3	-1	1	-2	-4	-2	10	-7	-7	6	6	-	-11	-7	-2	-11	-1	13	10

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Quadratic twists for elliptic curve 854c1

-4	8	-3	5	-7	-11	61
6832k1	27328a1	7686f1	21350h1	5978i1	103334k1	52094e1

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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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