Cremona's table of elliptic curves

16240 = 2⁴ · 5 · 7 · 29

Field	Data	Notes
Atkin-Lehner	2- 5- 7+ 29+	Signs for the Atkin-Lehner involutions
Class	16240r	Isogeny class
Conductor	16240	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	135030061418075600 = 24 · 52 · 712 · 293	Discriminant
Eigenvalues	2-  2 5- 7+ -6  2  6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-164025,-18417100]	[a1,a2,a3,a4,a6]
Generators	[2946700517213370833400:3799581831126152731205:6495073849682210304]	Generators of the group modulo torsion
j	30502575902160633856/8439378838629725	j-invariant
L	6.9617156062531	L(r)(E,1)/r!
Ω	0.24217934771417	Real period
R	28.74611593417	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	4060g3 64960be3 81200br3 113680bc3	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 16240r3

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

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Quadratic twists for elliptic curve 16240r3

-4	8	5	-7
4060g3	64960be3	81200br3	113680bc3

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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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