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	8	Product of Tamagawa factors cp
Δ	487265625 = 34 · 57 · 7 · 11	Discriminant
Eigenvalues	-1 3+ 5+ 7- 11-  2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-51338,-4498594]	[a1,a2,a3,a4,a6]
Generators	[375:5212:1]	Generators of the group modulo torsion
j	957681397954009/31185	j-invariant
L	2.2321956273578	L(r)(E,1)/r!
Ω	0.31716830047145	Real period
R	3.5189450270405	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	92400gb4 17325w4 1155h3 40425cp4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5775i3

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 5775i3

-4	-3	5	-7	-11
92400gb4	17325w4	1155h3	40425cp4	63525f4

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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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