Cremona's table of elliptic curves

8294 = 2 · 11 · 13 · 29

Field	Data	Notes
Atkin-Lehner	2- 11+ 13+ 29-	Signs for the Atkin-Lehner involutions
Class	8294b	Isogeny class
Conductor	8294	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	416	Modular degree for the optimal curve
Δ	-16588 = -1 · 22 · 11 · 13 · 29	Discriminant
Eigenvalues	2-  0  0  1 11+ 13+ -1  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-10,-11]	[a1,a2,a3,a4,a6]
Generators	[13:37:1]	Generators of the group modulo torsion
j	-100544625/16588	j-invariant
L	6.2590192770353	L(r)(E,1)/r!
Ω	1.3409327399074	Real period
R	2.3338304341303	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	66352k1 74646q1 91234j1 107822k1	Quadratic twists by: -4 -3 -11 13

Hecke Eigenvalues for elliptic curve 8294b1

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
-	0	0	1	+	+	-1	6	-3	-	7	-11	-4	-4	-1	3	4	-7	2	4	-6	7	4	-15	-10

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Quadratic twists for elliptic curve 8294b1

-4	-3	-11	13
66352k1	74646q1	91234j1	107822k1

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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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