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	5775i	Isogeny class
Conductor	5775	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	8238993984375 = 3 · 57 · 74 · 114	Discriminant
Eigenvalues	-1 3+ 5+ 7- 11-  2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-5088,18906]	[a1,a2,a3,a4,a6]
Generators	[-66:302:1]	Generators of the group modulo torsion
j	932288503609/527295615	j-invariant
L	2.2321956273578	L(r)(E,1)/r!
Ω	0.6343366009429	Real period
R	0.87973625676012	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	92400gb3 17325w3 1155h4 40425cp3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5775i4

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

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Quadratic twists for elliptic curve 5775i4

-4	-3	5	-7	-11
92400gb3	17325w3	1155h4	40425cp3	63525f3

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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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