Cremona's table of elliptic curves

10450 = 2 · 5² · 11 · 19

Field	Data	Notes
Atkin-Lehner	2+ 5- 11- 19+	Signs for the Atkin-Lehner involutions
Class	10450m	Isogeny class
Conductor	10450	Conductor
∏ cp	9	Product of Tamagawa factors cp
deg	15120	Modular degree for the optimal curve
Δ	-1264450000000 = -1 · 27 · 58 · 113 · 19	Discriminant
Eigenvalues	2+  2 5- -1 11-  0  2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-4075,112125]	[a1,a2,a3,a4,a6]
Generators	[-15:420:1]	Generators of the group modulo torsion
j	-19165185625/3236992	j-invariant
L	4.5805839941822	L(r)(E,1)/r!
Ω	0.82922347364618	Real period
R	0.61377155050066	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	83600cq1 94050dp1 10450ba1 114950do1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 10450m1

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	-	-1	-	0	2	+	-2	-2	-8	5	11	-6	6	-6	2	-1	10	-9	6	-10	-8	2	6

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Quadratic twists for elliptic curve 10450m1

-4	-3	5	-11
83600cq1	94050dp1	10450ba1	114950do1

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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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