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	5775n	Isogeny class
Conductor	5775	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	907970765625 = 34 · 56 · 72 · 114	Discriminant
Eigenvalues	1 3- 5+ 7+ 11+ -6 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-7101,-226277]	[a1,a2,a3,a4,a6]
j	2533811507137/58110129	j-invariant
L	2.0832599646327	L(r)(E,1)/r!
Ω	0.52081499115816	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	92400ev4 17325u3 231a3 40425k4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5775n3

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
1	-	+	+	+	-6	-2	4	0	-2	8	-6	10	4	8	-6	4	-10	12	0	-2	16	-4	18	-2

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Quadratic twists for elliptic curve 5775n3

-4	-3	5	-7	-11
92400ev4	17325u3	231a3	40425k4	63525bv4

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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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