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	10736a	Isogeny class
Conductor	10736	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1344	Modular degree for the optimal curve
Δ	-10478336 = -1 · 28 · 11 · 612	Discriminant
Eigenvalues	2+ -1  1  0 11+ -2  6  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,55,-11]	[a1,a2,a3,a4,a6]
Generators	[10:61:8]	Generators of the group modulo torsion
j	70575104/40931	j-invariant
L	3.8350998037268	L(r)(E,1)/r!
Ω	1.3719056543137	Real period
R	1.397727238629	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	5368b1 42944y1 96624k1 118096j1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 10736a1

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	1	0	+	-2	6	6	-3	-6	5	-3	0	2	-8	-2	11	+	3	-5	-2	-4	0	9	-3

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Quadratic twists for elliptic curve 10736a1

-4	8	-3	-11
5368b1	42944y1	96624k1	118096j1

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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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