Cremona's table of elliptic curves

5775 = 3 · 5² · 7 · 11

Field	Data	Notes
Atkin-Lehner	3- 5+ 7+ 11-	Signs for the Atkin-Lehner involutions
Class	5775r	Isogeny class
Conductor	5775	Conductor
∏ cp	50	Product of Tamagawa factors cp
deg	9600	Modular degree for the optimal curve
Δ	-21402168046875 = -1 · 35 · 57 · 7 · 115	Discriminant
Eigenvalues	0 3- 5+ 7+ 11-  0 -3 -3	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-3283,232969]	[a1,a2,a3,a4,a6]
Generators	[23:412:1]	Generators of the group modulo torsion
j	-250523582464/1369738755	j-invariant
L	3.7746599228599	L(r)(E,1)/r!
Ω	0.58864073907813	Real period
R	0.12825004021201	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	92400ea1 17325i1 1155d1 40425t1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5775r1

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	-	+	+	-	0	-3	-3	1	-7	6	8	-2	5	6	3	-5	-7	-6	-10	-12	-16	3	3	1

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Quadratic twists for elliptic curve 5775r1

-4	-3	5	-7	-11
92400ea1	17325i1	1155d1	40425t1	63525bq1

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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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