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	14450be	Isogeny class
Conductor	14450	Conductor
∏ cp	96	Product of Tamagawa factors cp
deg	138240	Modular degree for the optimal curve
Δ	-427627520000000 = -1 · 216 · 57 · 174	Discriminant
Eigenvalues	2- -3 5+  1  2  6 17-  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-30255,2264247]	[a1,a2,a3,a4,a6]
Generators	[-21:1710:1]	Generators of the group modulo torsion
j	-2346853689/327680	j-invariant
L	5.1338986718743	L(r)(E,1)/r!
Ω	0.51294363252331	Real period
R	0.10425728632654	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	115600cm1 2890f1 14450y1	Quadratic twists by: -4 5 17

Hecke Eigenvalues for elliptic curve 14450be1

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
-	-3	+	1	2	6	-	6	-3	-6	0	-10	9	-12	-8	-12	-6	-2	11	-6	-12	0	-9	-3	-10

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Quadratic twists for elliptic curve 14450be1

-4	5	17
115600cm1	2890f1	14450y1

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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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