Cremona's table of elliptic curves

14350 = 2 · 5² · 7 · 41

Field	Data	Notes
Atkin-Lehner	2- 5+ 7- 41+	Signs for the Atkin-Lehner involutions
Class	14350s	Isogeny class
Conductor	14350	Conductor
∏ cp	160	Product of Tamagawa factors cp
Δ	4845315240500000 = 25 · 56 · 78 · 412	Discriminant
Eigenvalues	2- -2 5+ 7- -6  4  2  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-55538,3758692]	[a1,a2,a3,a4,a6]
Generators	[42:1204:1]	Generators of the group modulo torsion
j	1212480836738137/310100175392	j-invariant
L	4.9796150740378	L(r)(E,1)/r!
Ω	0.40541923332025	Real period
R	0.30706578923601	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	114800bd2 129150bp2 574b2 100450bx2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 14350s2

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

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Quadratic twists for elliptic curve 14350s2

-4	-3	5	-7
114800bd2	129150bp2	574b2	100450bx2

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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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