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	8450r	Isogeny class
Conductor	8450	Conductor
∏ cp	36	Product of Tamagawa factors cp
deg	60480	Modular degree for the optimal curve
Δ	-411228681011200 = -1 · 218 · 52 · 137	Discriminant
Eigenvalues	2-  2 5+  5  3 13+ -3  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-22058,-1603529]	[a1,a2,a3,a4,a6]
j	-9836106385/3407872	j-invariant
L	6.930413850965	L(r)(E,1)/r!
Ω	0.19251149586014	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	67600ch1 76050bx1 8450k1 650b1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 8450r1

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	+	5	3	+	-3	4	-6	9	-5	2	0	-2	-9	9	9	-1	5	0	14	-16	-15	6	8

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Quadratic twists for elliptic curve 8450r1

-4	-3	5	13
67600ch1	76050bx1	8450k1	650b1

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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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