Cremona's table of elliptic curves

8745 = 3 · 5 · 11 · 53

Field	Data	Notes
Atkin-Lehner	3- 5+ 11- 53+	Signs for the Atkin-Lehner involutions
Class	8745i	Isogeny class
Conductor	8745	Conductor
∏ cp	40	Product of Tamagawa factors cp
Δ	111803741818065 = 320 · 5 · 112 · 53	Discriminant
Eigenvalues	1 3- 5+ -4 11- -2  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-172244,-27524203]	[a1,a2,a3,a4,a6]
Generators	[3894:14087:8]	Generators of the group modulo torsion
j	565135247515245603769/111803741818065	j-invariant
L	5.0651181298682	L(r)(E,1)/r!
Ω	0.2343521741097	Real period
R	2.1613275614406	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	26235j4 43725h4 96195t4	Quadratic twists by: -3 5 -11

Hecke Eigenvalues for elliptic curve 8745i3

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

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Quadratic twists for elliptic curve 8745i3

-3	5	-11
26235j4	43725h4	96195t4

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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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