Cremona's table of elliptic curves

14045 = 5 · 53²

Field	Data	Notes
Atkin-Lehner	5+ 53+	Signs for the Atkin-Lehner involutions
Class	14045a	Isogeny class
Conductor	14045	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	1620	Modular degree for the optimal curve
Δ	351125 = 53 · 532	Discriminant
Eigenvalues	-2  0 5+  2  0  0  0 -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-53,-146]	[a1,a2,a3,a4,a6]
Generators	[-4:1:1]	Generators of the group modulo torsion
j	5861376/125	j-invariant
L	2.171629742489	L(r)(E,1)/r!
Ω	1.771715367366	Real period
R	1.2257215704561	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	126405t1 70225e1 14045e1	Quadratic twists by: -3 5 53

Hecke Eigenvalues for elliptic curve 14045a1

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	0	+	2	0	0	0	-1	2	5	5	-4	3	-2	-8	+	-11	-1	-6	8	10	-5	-14	1	16

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Quadratic twists for elliptic curve 14045a1

-3	5	53
126405t1	70225e1	14045e1

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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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