Cremona's table of elliptic curves

5742 = 2 · 3² · 11 · 29

Field	Data	Notes
Atkin-Lehner	2+ 3+ 11- 29+	Signs for the Atkin-Lehner involutions
Class	5742c	Isogeny class
Conductor	5742	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	120892068 = 22 · 33 · 113 · 292	Discriminant
Eigenvalues	2+ 3+  0 -4 11-  2 -6  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-85182,9590400]	[a1,a2,a3,a4,a6]
j	2531665445447410875/4477484	j-invariant
L	0.80238436699234	L(r)(E,1)/r!
Ω	1.2035765504885	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	45936v2 5742q4 63162bp2	Quadratic twists by: -4 -3 -11

Hecke Eigenvalues for elliptic curve 5742c2

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

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Quadratic twists for elliptic curve 5742c2

-4	-3	-11
45936v2	5742q4	63162bp2

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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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