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	10	Product of Tamagawa factors cp
Δ	1.7828816993957E+19	Discriminant
Eigenvalues	2-  1 -4  2 11+ -1  3  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-3006080,1994768564]	[a1,a2,a3,a4,a6]
Generators	[-244:52094:1]	Generators of the group modulo torsion
j	733441552889589371521/4352738523915232	j-invariant
L	4.0356135254309	L(r)(E,1)/r!
Ω	0.21960892824475	Real period
R	1.8376363646442	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	1342c2 42944v2 96624bu2 118096y2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 10736f2

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 10736f2

-4	8	-3	-11
1342c2	42944v2	96624bu2	118096y2

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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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