Cremona's table of elliptic curves

5610 = 2 · 3 · 5 · 11 · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 11- 17-	Signs for the Atkin-Lehner involutions
Class	5610bi	Isogeny class
Conductor	5610	Conductor
∏ cp	288	Product of Tamagawa factors cp
Δ	1019696040000 = 26 · 36 · 54 · 112 · 172	Discriminant
Eigenvalues	2- 3- 5+  0 11- -6 17-  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-2971,38801]	[a1,a2,a3,a4,a6]
Generators	[-22:317:1]	Generators of the group modulo torsion
j	2900285849172529/1019696040000	j-invariant
L	6.3317226804166	L(r)(E,1)/r!
Ω	0.80468768949282	Real period
R	0.43714148448818	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	44880bf2 16830x2 28050j2 61710x2	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 5610bi2

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

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Quadratic twists for elliptic curve 5610bi2

-4	-3	5	-11	17
44880bf2	16830x2	28050j2	61710x2	95370ci2

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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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