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	5775o	Isogeny class
Conductor	5775	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	-8616658779544921875 = -1 · 316 · 59 · 7 · 114	Discriminant
Eigenvalues	-1 3- 5+ 7+ 11+  2  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-296813,-154361508]	[a1,a2,a3,a4,a6]
j	-185077034913624841/551466161890875	j-invariant
L	1.5130078504453	L(r)(E,1)/r!
Ω	0.094562990652829	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	92400em3 17325q4 1155f4 40425m3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5775o4

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	-	+	+	+	2	6	4	4	-2	-4	2	-2	12	0	2	0	-14	8	-16	-10	16	4	-6	-2

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Quadratic twists for elliptic curve 5775o4

-4	-3	5	-7	-11
92400em3	17325q4	1155f4	40425m3	63525bs3

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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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