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	32	Product of Tamagawa factors cp
Δ	86830734375 = 38 · 56 · 7 · 112	Discriminant
Eigenvalues	1 3- 5+ 7+ 11+ -6 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-112976,-14625277]	[a1,a2,a3,a4,a6]
j	10206027697760497/5557167	j-invariant
L	2.0832599646327	L(r)(E,1)/r!
Ω	0.26040749557908	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	92400ev6 17325u5 231a5 40425k6	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5775n5

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 5775n5

-4	-3	5	-7	-11
92400ev6	17325u5	231a5	40425k6	63525bv6

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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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