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	854a	Isogeny class
Conductor	854	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	240	Modular degree for the optimal curve
Δ	21425152 = 210 · 73 · 61	Discriminant
Eigenvalues	2+  1 -2 7+  3  0  3 -3	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-722,7396]	[a1,a2,a3,a4,a6]
Generators	[13:9:1]	Generators of the group modulo torsion
j	41540367914137/21425152	j-invariant
L	1.8547964065189	L(r)(E,1)/r!
Ω	2.1225419878005	Real period
R	0.43692808367974	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	6832j1 27328d1 7686q1 21350u1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 854a1

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	+	3	0	3	-3	-1	-6	-6	-6	0	-11	-3	4	0	+	1	-1	0	-5	9	3	2

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Quadratic twists for elliptic curve 854a1

-4	8	-3	5	-7	-11	61
6832j1	27328d1	7686q1	21350u1	5978f1	103334bi1	52094k1

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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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