Cremona's table of elliptic curves

14450 = 2 · 5² · 17²

Field	Data	Notes
Atkin-Lehner	2+ 5- 17-	Signs for the Atkin-Lehner involutions
Class	14450p	Isogeny class
Conductor	14450	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	12240	Modular degree for the optimal curve
Δ	-20880250 = -1 · 2 · 53 · 174	Discriminant
Eigenvalues	2+ -2 5-  3  3 -3 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-3041,64278]	[a1,a2,a3,a4,a6]
Generators	[32:-14:1]	Generators of the group modulo torsion
j	-297756989/2	j-invariant
L	2.5721121454828	L(r)(E,1)/r!
Ω	1.925621336708	Real period
R	0.667865508252	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	115600dg1 14450bl1 14450n2	Quadratic twists by: -4 5 17

Hecke Eigenvalues for elliptic curve 14450p1

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	-	3	3	-3	-	-4	-5	-8	8	2	6	-10	3	3	11	12	-8	-12	-2	14	16	5	-18

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Quadratic twists for elliptic curve 14450p1

-4	5	17
115600dg1	14450bl1	14450n2

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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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