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	8450o	Isogeny class
Conductor	8450	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1680	Modular degree for the optimal curve
Δ	-10562500 = -1 · 22 · 56 · 132	Discriminant
Eigenvalues	2-  0 5+  4 -4 13+ -3  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,20,147]	[a1,a2,a3,a4,a6]
j	351/4	j-invariant
L	3.3648197729522	L(r)(E,1)/r!
Ω	1.6824098864761	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	67600bk1 76050bs1 338a1 8450b1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 8450o1

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	+	4	-4	+	-3	0	4	-1	-4	3	9	8	-8	9	4	7	4	8	11	-4	0	6	2

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Quadratic twists for elliptic curve 8450o1

-4	-3	5	13
67600bk1	76050bs1	338a1	8450b1

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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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