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	14450o	Isogeny class
Conductor	14450	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	55296	Modular degree for the optimal curve
Δ	-4103386730000 = -1 · 24 · 54 · 177	Discriminant
Eigenvalues	2+  3 5-  1  4  3 17+  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,2258,87716]	[a1,a2,a3,a4,a6]
j	84375/272	j-invariant
L	4.4147685755731	L(r)(E,1)/r!
Ω	0.55184607194664	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	115600dd1 14450bb1 850e1	Quadratic twists by: -4 5 17

Hecke Eigenvalues for elliptic curve 14450o1

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	4	3	+	6	0	0	9	-4	-6	12	-10	-9	0	14	-8	15	12	-3	0	-6	-16

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Quadratic twists for elliptic curve 14450o1

-4	5	17
115600dd1	14450bb1	850e1

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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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