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	8450m	Isogeny class
Conductor	8450	Conductor
∏ cp	128	Product of Tamagawa factors cp
deg	32256	Modular degree for the optimal curve
Δ	1254970340000000 = 28 · 57 · 137	Discriminant
Eigenvalues	2-  0 5+  0  0 13+ -2  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-28255,-653753]	[a1,a2,a3,a4,a6]
j	33076161/16640	j-invariant
L	3.1052616837635	L(r)(E,1)/r!
Ω	0.38815771047043	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	67600be1 76050y1 1690a1 650a1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 8450m1

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	0	+	-2	8	4	-2	4	6	-10	0	8	-6	-8	-2	4	12	10	-8	12	-10	-14

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Quadratic twists for elliptic curve 8450m1

-4	-3	5	13
67600be1	76050y1	1690a1	650a1

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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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