Cremona's table of elliptic curves

14365 = 5 · 13² · 17

Field	Data	Notes
Atkin-Lehner	5- 13+ 17-	Signs for the Atkin-Lehner involutions
Class	14365b	Isogeny class
Conductor	14365	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	9216	Modular degree for the optimal curve
Δ	2051393825 = 52 · 136 · 17	Discriminant
Eigenvalues	-1  2 5-  2 -2 13+ 17-  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-1440,-21520]	[a1,a2,a3,a4,a6]
Generators	[-186:149:8]	Generators of the group modulo torsion
j	68417929/425	j-invariant
L	4.9056185004817	L(r)(E,1)/r!
Ω	0.77530014773789	Real period
R	3.1636899043518	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	129285q1 71825d1 85a1	Quadratic twists by: -3 5 13

Hecke Eigenvalues for elliptic curve 14365b1

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	-	2	-2	+	-	0	6	-6	10	-2	-10	4	-12	-10	-8	-14	-8	2	14	-14	-4	-6	-2

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Quadratic twists for elliptic curve 14365b1

-3	5	13
129285q1	71825d1	85a1

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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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