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	10450be	Isogeny class
Conductor	10450	Conductor
∏ cp	150	Product of Tamagawa factors cp
Δ	-111563116544000 = -1 · 215 · 53 · 11 · 195	Discriminant
Eigenvalues	2- -1 5- -2 11- -1 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,1747,508131]	[a1,a2,a3,a4,a6]
Generators	[55:852:1]	Generators of the group modulo torsion
j	4717119482011/892504932352	j-invariant
L	5.0594178818916	L(r)(E,1)/r!
Ω	0.45766167414917	Real period
R	1.8424883735704	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	5	Number of elements in the torsion subgroup
Twists	83600cj2 94050bx2 10450o2 114950bn2	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 10450be2

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
-	-1	-	-2	-	-1	-2	-	-1	0	7	8	7	-1	-7	-6	0	7	13	-8	-1	0	-11	0	-2

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Quadratic twists for elliptic curve 10450be2

-4	-3	5	-11
83600cj2	94050bx2	10450o2	114950bn2

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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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