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	8450s	Isogeny class
Conductor	8450	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	322560	Modular degree for the optimal curve
Δ	784356462500000000 = 28 · 511 · 137	Discriminant
Eigenvalues	2- -2 5+ -4  2 13+ -2 -6	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-3553313,-2578035383]	[a1,a2,a3,a4,a6]
j	65787589563409/10400000	j-invariant
L	0.87970142316051	L(r)(E,1)/r!
Ω	0.10996267789506	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	67600by1 76050bu1 1690e1 650e1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 8450s1

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
-	-2	+	-4	2	+	-2	-6	-6	2	6	-2	-10	10	-12	-2	-10	2	-12	-10	10	-4	0	14	14

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Quadratic twists for elliptic curve 8450s1

-4	-3	5	13
67600by1	76050bu1	1690e1	650e1

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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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