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	16240q	Isogeny class
Conductor	16240	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	29382056560640000 = 214 · 54 · 76 · 293	Discriminant
Eigenvalues	2-  2 5- 7+  0  2  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-8321920,9243014400]	[a1,a2,a3,a4,a6]
Generators	[1440:15600:1]	Generators of the group modulo torsion
j	15560889758045383006081/7173353652500	j-invariant
L	7.3059796458561	L(r)(E,1)/r!
Ω	0.30412691505124	Real period
R	3.0028498318807	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	2030b4 64960bc4 81200bp4 113680ba4	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 16240q4

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

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Quadratic twists for elliptic curve 16240q4

-4	8	5	-7
2030b4	64960bc4	81200bp4	113680ba4

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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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