Cremona's table of elliptic curves

5735 = 5 · 31 · 37

Field	Data	Notes
Atkin-Lehner	5+ 31+ 37+	Signs for the Atkin-Lehner involutions
Class	5735a	Isogeny class
Conductor	5735	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	13056	Modular degree for the optimal curve
Δ	19014661328125 = 58 · 312 · 373	Discriminant
Eigenvalues	0 -1 5+  3  5 -6 -4  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-7771,-157148]	[a1,a2,a3,a4,a6]
Generators	[-44:312:1]	Generators of the group modulo torsion
j	51905134932557824/19014661328125	j-invariant
L	2.6037415931685	L(r)(E,1)/r!
Ω	0.52410193604954	Real period
R	1.2420015144356	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	91760f1 51615e1 28675a1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 5735a1

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	-1	+	3	5	-6	-4	2	-4	8	+	+	3	2	-9	-13	14	0	4	9	-3	14	-9	12	-2

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Quadratic twists for elliptic curve 5735a1

-4	-3	5
91760f1	51615e1	28675a1

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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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