Cremona's table of elliptic curves

10736 = 2⁴ · 11 · 61

Field	Data	Notes
Atkin-Lehner	2- 11+ 61-	Signs for the Atkin-Lehner involutions
Class	10736f	Isogeny class
Conductor	10736	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	5496832 = 213 · 11 · 61	Discriminant
Eigenvalues	2-  1 -4  2 11+ -1  3  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1876116000,31277278787444]	[a1,a2,a3,a4,a6]
Generators	[122798684:-16768430:4913]	Generators of the group modulo torsion
j	178296503348692983836197044001/1342	j-invariant
L	4.0356135254309	L(r)(E,1)/r!
Ω	0.21960892824475	Real period
R	9.1881818232208	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1342c3 42944v3 96624bu3 118096y3	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 10736f3

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	-4	2	+	-1	3	0	-4	10	-7	3	-8	11	12	9	0	-	-8	3	14	0	-14	0	-17

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Quadratic twists for elliptic curve 10736f3

-4	8	-3	-11
1342c3	42944v3	96624bu3	118096y3

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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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