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	18	Product of Tamagawa factors cp
Δ	-24134045000 = -1 · 23 · 54 · 136	Discriminant
Eigenvalues	2-  1 5- -2  3 13+ -3 -5	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-21213,-1190983]	[a1,a2,a3,a4,a6]
Generators	[352:5739:1]	Generators of the group modulo torsion
j	-349938025/8	j-invariant
L	7.042458782097	L(r)(E,1)/r!
Ω	0.19779637756962	Real period
R	1.9780327371202	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	67600da2 76050cr2 8450d4 50a2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 8450x2

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 8450x2

-4	-3	5	13
67600da2	76050cr2	8450d4	50a2

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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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