Cremona's table of elliptic curves

8450 = 2 · 5² · 13²

Field	Data	Notes
Atkin-Lehner	2- 5- 13+	Signs for the Atkin-Lehner involutions
Class	8450x	Isogeny class
Conductor	8450	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	4320	Modular degree for the optimal curve
Δ	-6033511250 = -1 · 2 · 54 · 136	Discriminant
Eigenvalues	2-  1 5- -2  3 13+ -3 -5	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-88,-3758]	[a1,a2,a3,a4,a6]
Generators	[38310:203249:1000]	Generators of the group modulo torsion
j	-25/2	j-invariant
L	7.042458782097	L(r)(E,1)/r!
Ω	0.59338913270886	Real period
R	5.9340982113607	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	67600da1 76050cr1 8450d3 50a1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 8450x1

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	+	-3	-5	6	0	-2	-2	3	-4	-12	6	0	2	13	-12	-11	-10	9	-15	-2

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Quadratic twists for elliptic curve 8450x1

-4	-3	5	13
67600da1	76050cr1	8450d3	50a1

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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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